Benchmarks Geometry
Benchmark Learning Standards for Geometry
Note: The parentheses at the end of a learning standard contain the code number(s) for the corresponding standard(s) in the two-year grade spans.
Q1 Q2 Q3 Q4
Geometry
Students engage in problem solving, communicating, reasoning, connecting, and representing as they:
Recognize special types of polygons (e.g., isosceles triangles, parallelograms, and
rhombuses). Apply properties of sides, diagonals, and angles in special polygons;
G.G.1 identify their parts and special segments (e.g., altitudes, midsegments); determine I M
interior angles for regular polygons. Draw and label sets of points such as line
segments, rays, and circles. Detect symmetries of geometric figures.
Define: line, line segment, ray, angle, equilateral, isosceles, right and scalene triangles,
polygon, regular polygon, pentagon, hexagon, heptagon, octagon, nonagon, decagon, M
concave, convex
Draw and correctly label lines, line segments and rays M
Distinguish between lines, line segments and rays M
Draw and correctly label angles, triangles, circles and a variety of polygons (regular,
M
concave, convex)
Draw and identify sides, angles and diagonals of polygons M
Draw and identify radii and diameters of circles M
Draw and identify altitudes, medians and midsegments M
Distinguish between equilateral, scalene, isosceles and right triangles M
Use the Polygon Sum Theorem to determine the sum of interior angles M
Use the Polygon Sum Theorem to find missing angles of a polygon M
Calculate the measure of each angle in a regular polygon M
Classify polygons given the characteristics of sides, angles and diagonals M
Define: trapezoid, isosceles trapezoid, parallelogram, rectangle, kites, rhombus, square M
Distinguish between all types of quadrilaterals M
Show how quadrilaterals are related (e.g.. Use the Quadrilateral Hierarchy) M
Apply properties of diagonals in various quadrilateral M
Define: reflection symmetry, rotational symmetry I M
Determine a figure's type of symmetry I M
Draw a figure's line(s) of symmetry and/or center of symmetry I M
Benchmarks Geometry
Write simple proofs of theorems in geometric situations, such as theorems about
congruent and similar figures, parallel or perpendicular lines. Distinguish between
G.G.2 postulates and theorems. Use inductive and deductive reasoning, as well as proof by I I M
contradiction. Given a conditional statement, write its inverse, converse, and contra
positive.
Distinguish between a definition, theorem and a postulate M
Write a conditional, biconditional, converse and contrapositive M
Apply the properties of conditional statements when using conjectures M
Prove two lines are parallel M
Prove two lines are perpendicular M
Prove triangles are congruent M
Prove triangles are similar M
Prove a figure is a specific type of polygon (e.g.. Prove a figure is a rhombus by
showing all four sides are congruent) M
Use a variety of techniques to prove including inductive reasoning, deductive
reasoning and counterexample or contradiction. M
G.G.3 Apply formulas for a rectangular coordinate system to prove theorems I M
Calculate the slope of a line or line segment given 2 coordinates M
Calculate the distance between two coordinates M
Calculate the midpoint of a line segment given the coordinates of the endpoints M
Prove two lines are parallel, perpendicular or non-perpendicular intersecting lines by
M
using slopes
Define: congruent M
Prove segments are congruent by using the distance formula M
Prove a segment has been bisected by using the midpoint or distance formula M
Prove a triangle is equilateral, isosceles or right by using the distance formula and/or
M
slopes
Prove a quadrilateral is a trapezoid, isosceles trapezoid, parallelogram, kite, rhombus,
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square or rectangle by using the distance formula and/or slopes
Draw congruent and similar figures using a compass, straightedge, protractor, or
G.G.4 computer software. Make conjectures about methods of construction. Justify the M
conjectures by logical arguments.
Draw congruent figures using a compass, straightedge, protractor or computer M
software
Draw similar figures using a compass, straightedge, protractor or computer software M
Construct geometric figures using only a compass and straightedge M
Benchmarks Geometry
Use appropriate methods of construction and explain their use M
Apply congruence and similarity correspondences (e.g., DABC @ DXYZ) and
G.G.5 (10.G.4) properties of the figures to find missing parts of geometric figures, and provide logical M
justification.
Define: similar figures, proportion M
Solve a proportion using the Means Extremes Theorem M
Find missing pieces of similar figures by using a proportion M
Use the properties of congruence to find missing pieces in two congruent figures M
Apply properties of angles, parallel lines, arcs, radii, chords, tangents, and secants to
G.G.6 I M
solve problems.
Define: complementary, supplementary, linear pair, vertical angles, parallel lines,
transversal, alternate interior angles (AIA), alternate exterior angles (AEA), M
corresponding angles
Define: radii, chord, tangent, secant, inscribed angle, exterior angle, central angle,
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major arc, minor arc
Calculate angle measures in problems involving complementary and supplementary
M
angles
Use the Linear Pair Theorem to calculate angle measures in a linear pair M
Use the Vertical Angle Theorem to calculate the measures of vertical angles M
Calculate a variety of angle measures (AIA, AEA, corresponding angles) when two
M
parallel lines are cut by a transversal
Given angle measures (AIA, AEA, corresponding angles), determine if two lines are
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parallel
Given angle measures (inscribed, exterior, central), calculate the length of an arc M
Given the length of an arc, calculate a variety of angle measures (inscribed, exterior,
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central)
Calculate lengths of radii, chords, tangents and secants M
Calculate parts of chords, tangents and secants when they intersect M
Solve simple triangle problems using the triangle angle sum property, and/or the
G.G.7 (10.G.5) M
Pythagorean theorem.
Use the Triangle Sum Property to find missing angles in a triangle M
Given two legs of a right triangle, calculate the length of the hypotenuse using the
M
Pythagorean Theorem
Given one leg and the hypotenuse of a right triangle, calculate the length of the other
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leg using The Pythagorean Theorem
Benchmarks Geometry
Use the properties of special triangles (e.g., isosceles, equilateral, 30º–60º–90º,
G.G.8 (10.G.6) I M
45º–45º–90º) to solve problems.
Given the length of one non-base side of an isosceles triangle, find the length of the
M
other non-base side
Use the Isosceles Base Angles Theorem to find base angles in an isosceles triangle M
Find the lengths of sides in an equilateral triangle M
Find the measures of angles in an equilateral triangle M
Find the measures of angles in a right triangle M
Given two legs of a right triangle, calculate the length of the hypotenuse using the
M
Pythagorean Theorem
Given one leg and the hypotenuse of a right triangle, calculate the length of the other
M
leg using The Pythagorean Theorem
Given the length of one side of a 45º–45º–90º triangle, find the lengths of the
M
remaining sides
Given the length of one side of a 30º–60º–90º triangle, find the lengths of the
M
remaining sides
Define the sine, cosine, and tangent of an acute angle. Apply to the solution of
G.G.9 M
problems.
Label the sides of a right triangle appropriately (opposite, adjacent, hypotenuse) M
Define: sine, cosine, and tangent of an acute angle M
Use SOHCAHTOA or another device to remember the ratios M
Create the sine, cosine or tangent ratio given a right triangle M
Find the sine, cosine or tangent ratio using a calculator M
Use inverse ratios to find angle measure corresponding to a given trig ratio value M
Solve for missing sides in a right triangle using the appropriate ratio M
Solve for missing angles in a right triangle using the appropriate ratio M
Model and solve real world problems using the appropriate trig ratio M
Apply the triangle inequality and other inequalities associated with triangles (e.g., the
G.G.10 M
longest side is opposite the greatest angle) to prove theorems and solve problems.
Determine the range of lengths of the side of a triangle given 2 sides M
Determine if a length is possible for the third side of a triangle given 2 sides M
Given three lengths, determine if a triangle could be made with them M
Determine the order of length of sides of a triangle given the angles M
Determine the order of the angles of a triangle given the lengths of sides M
Benchmarks Geometry
Demonstrate an understanding of the relationship between various representations of a
line. Determine a line’s slope and x- and y-intercepts from its graph or from a linear
equation that represents the line. Find a linear equation describing a line from a graph
G.G.11 (10.P.2) M
or a geometric description of the line, e.g., by using the “point-slope” or “slope y-
intercept” formulas. Explain the significance of a positive, negative, zero, or undefined
slope.
Define: x-axis, y-axis, intercept, line, horizontal, vertical, oblique, slope, rate of
M
change
Plot a point on the coordinate plane M
Identify a line as horizontal, vertical or oblique (increasing or decreasing) from its
M
graph
Identify a line as horizontal, vertical or oblique (increasing or decreasing) from its
M
equation
Calculate the slope of a line from two points using The Slope Formula M
Determine the slope of a line from an equation (in Slope-Intercept Form or Standard
M
Form)
Determine the slope of a line from its graph M
Identify the x and y - intercepts from a graph M
Identify the x and y - intercepts from an equation (in Slope-Intercept Form or Standard
M
Form)
Given a graph, write the equation of a line in Slope - Intercept Form M
Given a graph, write the equation of a line in Standard Form M
Write the equation of a line given one point on the line and the slope, using Point-
M
Slope Form
Write the equation of a line given two points, using Point-Slope form M
Translate between all forms of equations M
Define: positive slope, negative slope, zero slope and undefined (no) slope M
Classify the slope of a line as positive, negative, zero or undefined given a graph of the
M
line
Classify the slope of a line as positive, negative, zero or undefined given the equation
M
of the line
Identify a line as horizontal, vertical, oblique (increasing or decreasing) from its slope M
Using rectangular coordinates, calculate midpoints of segments, slopes of lines and
G.G12 (10.G.7) segments, and distances between two points, and apply the results to the solutions of I M
problems.
Benchmarks Geometry
Calculate the slope of a line or line segment given 2 coordinates M
Calculate the distance between two coordinates M
Calculate the length of a line segment using the distance formula M
Calculate the midpoint of a line segment given the coordinates of the endpoints M
Apply the distance formula to solve a word problem M
Apply the midpoint formula to solve a word problem M
Apply the slope formula to solve a word problem M
Find linear equations that represent lines either perpendicular or parallel to a given line
G.G.13 (10.G.8) M
and through a point, e.g., by using the “point-slope” form of the equation.
Define the relationship between the slopes of parallel lines M
Write the equation of a line parallel to a given line through a given point M
Determine if two lines are parallel given their slopes M
Determine if two lines are parallel given their equations M
Define the relationship between the slopes of perpendicular lines M
Write the equation of a line perpendicular to a given line through a given point M
Determine if two lines are perpendicular given their equations M
Determine if two lines are perpendicular given their slopes M
Demonstrate an understanding of the relationship between geometric and algebraic
G.G.14 M
representations of circles.
Given the center and radius (or diameter) of a circle, write an equation representing the
circle M
Given an equation of a circle in standard form, determine the center and radius M
Given an equation of a circle in standard form, graph the circle M
Given a graph of a circle, determine the center and radius (or diameter) of the circle M
Given a graph of a circle, write an equation in standard form to represent the circle M
Draw the results, and interpret transformations on figures in the coordinate plane, e.g.,
G.G.15 (10.G.9) translations, reflections, rotations, scale factors, and the results of successive M
transformations. Apply transformations to the solution of problems.
Define: transformation, translation, reflection, rotation, scale/size change, scale factor,
M
magnitude, isometry, preimage, image, orientation, vector
Use proper notation for reflections over a given line, multiple reflections, rotations,
M
scale/size changes and vectors
Determine the orientation of a given figure M
Reflect a point over a given line M
Reflect a figure over a given line M
Benchmarks Geometry
Reflect a point over more than one line M
Reflect a figure over more than one line (include both parallel and intersecting lines) M
Rotate a point about a given point a given magnitude M
Rotate a figure about a given point a given magnitude M
Translate a point using reflections and using vectors M
Translate a figure using reflections and using vectors M
Given a preimage and a rotated image, determine the magnitude of the rotation M
M
Given a preimage and a translated image, determine the magnitude of the translation
Given a preimage and a reflected image, find the line of reflection M
Scale/Size change a figure on the coordinate plane M
Given a preimage and a scale/size changed image, determine the scale change factor M
Determine if two figures have the same orientation M
Determine if a transformation is an isometry M
Given an image and a preimage, determine the type of transformation that has been
M
applied
G.G.16 Demonstrate the ability to visualize solid objects and recognize their projections and
M
(10.G.10) cross sections.
Define: net, cross section, projection M
Given a solid object, draw its net M
Given a net, determine the solid object it represents M
Determine if a solid object can be made from a given net M
Determine the view of a solid object from above, from the left and from the right M
Given a projection and a solid object, determine if it is a view from above, from the
M
left or from the right
Given a projection, determine if it represents a particular solid object M
Determine the cross section of a plane and a given solid. Orient the intersecting plane
M
parallel to the base of the object, intersecting planethe basecreates object andcross
Determine the orientation of the perpendicular to which of the the given obliquely
section M
Determine if a given cross section can be made from the intersection of a plane and a
M
solid object
G.G.17
Use vertex-edge graphs to model and solve problems. M
(10.G.11)
Define: network, node, odd node, even node, traversable M
Determine the type of nodes in a network M
Benchmarks Geometry
Determine if a network is traversable M
Identify starting point and ending point on a traversable network. M
Identify the path to get from the starting point to the ending point of a traversable
M
network
Model a real world situation with a network and solve a related problem (e.g. bus
M
routes)
Use the notion of vectors to solve problems. Describe addition of vectors and
G.G.18 (12.G.3) multiplication of a vector by a scalar, both symbolically and pictori-ally. Use vector M
methods to obtain geometric results.
Define: vector, horizontal component, vertical component M
Use vectors to translate points and figures M
Given a completed translation, identify the vector used M
Add vectors symbolically M
Add vectors pictorially M
Multiply a vector by a scalar symbolically M
Multiply a vector by a scalar pictorially M
Learning Standards for Measurement
Students engage in problem solving, communicating, reasoning, connecting, and representing as they:
Calculate perimeter, circumference, and area of common geometric figures such as
G.M.1 (10.M.1) I M
parallelograms, trapezoids, circles, and triangles.
Calculate the perimeter of any triangle I M
Calculate the perimeter of any quadrilateral I M
Calculate the perimeter of any regular polygon I M
Calculate the perimeter of a basic non-regular polygon (e.g.. pentagons, octagons, etc.) I M
Calculate the circumference of a circle I M
Given the perimeter of a figure, determine the length of missing sides I M
Given the circumference of a circle, calculate the length of the radius (or diameter) I M
Calculate the area of any triangle M
Calculate the area of any trapezoid, parallelogram, rhombus, kite, rectangle or square M
Calculate the area of a regular polygon by breaking it up M
Calculate the area of any irregular polygon by breaking it up M
Calculate the area of a circle M
Given the area of a figure, calculate the length of a particular side M
Given the area of a circle, calculate the length of the radius (or diameter) M
Benchmarks Geometry
Given the measurement of a 2-D object, calculate another measure (e.g.. Find the
M
perimeter of a square given its area)
Solve a word problem by calculating perimeters, circumferences or areas M
Given the formula, find the lateral area, surface area, and volume of prisms, pyramids,
G.M.2 (10.M.2) spheres, cylinders, and cones, e.g., find the volume of a sphere with a specified surface M
area.
Define: lateral area, surface area, volume, base, edge, face M
Identify and label (i.e. base, edge, radius, etc.) prisms, pyramids, cylinders, cones and
M
spheres
Identify the difference between lateral area and surface area or prisms, pyramids,
M
cylinders and cones
Calculate the lateral area of prisms, pyramids, cylinders and cones M
Calculate the surface area of prisms, pyramids, cylinders, cones and spheres M
Calculate the volume of prisms, pyramids, cylinders, cones and spheres M
Given the measurement of a 3-D object, calculate another measure (e.g.. Find the
M
lateral area of a cylinder given its volume and height)
Solve word problems by calculating the lateral area of prisms, pyramids, cylinders and
M
cones
Solve word problems by calculating the surface area of prisms, pyramids, cylinders,
M
cones and spheres
Solve word problems by calculating the volume of prisms, pyramids, cylinders, cones
M
and spheres
Relate changes in the measurement of one attribute of an object to changes in other
G.M.3 (10.M.3) attributes, e.g., how changing the radius or height of a cylinder affects its surface area M
or volume.
Determine how changing one attribute of an object affects its perimeter M
Determine how changing one attribute of an object affects its area M
Determine how changing one attribute of an object affects its lateral area M
Determine how changing one attribute of an object affects its surface area M
Determine how changing one attribute of an object affects its volume M
Describe the effects of approximate error in measurement and rounding on
G.M.4 (10.M.4) M
measurements and on computed values from measurements.
Describe the effect of measurement errors when calculating perimeter, area and M
volume the effect of rounding when calculating perimeter, area and volume
Describe M
Benchmarks Geometry
Use dimensional analysis for unit conversion and to confirm that expressions and
G.M.5 (12.M.2) M
equations make sense.
Convert units in the metric system (e.g. cm to m) M
Convert units in the standard system (e.g. ft to mi) M
Convert between two measurement systems (e.g.. centimeters to inches) M
Use appropriate units in measurements (ex. volume uses cubic units) M
Determine whether given units in a problem make sense or need to be converted (ex.
M
length given in inches, width given in feet, calculate the area)
Quarter 1
Benchmark Mastery Skills
Geometry - Quarter 1
Standard Q1 Q2 Q3 Q4
Note: The parentheses at the end of a learning standard contain the code number(s) for the corresponding standard(s) in the two-year grade spans.
Define: line, line segment, ray, angle, equilateral, isosceles, right and scalene triangles,
G.G.1 polygon, regular polygon, pentagon, hexagon, heptagon, octagon, nonagon, decagon, M
concave, convex
G.G.1 Draw and correctly label lines, line segments and rays M
G.G.1 Distinguish between lines, line segments and rays M
Draw and correctly label angles, triangles, circles and a variety of polygons (regular,
G.G.1 M
concave, convex)
G.G.1 Draw and identify sides, angles and diagonals of polygons M
G.G.1 Draw and identify radii and diameters of circles M
G.G.1 Draw and identify altitudes, medians and midsegments M
G.G.1 Distinguish between equilateral, scalene, isosceles and right triangles M
G.G.1 Use the Polygon Sum Theorem to determine the sum of interior angles M
G.G.1 Use the Polygon Sum Theorem to find missing angles of a polygon M
G.G.1 Calculate the measure of each angle in a regular polygon M
G.G.1 Classify polygons given the characteristics of sides, angles and diagonals M
G.G.1 Define: reflection symmetry, rotational symmetry I M
G.G.1 Determine a figure's type of symmetry I M
G.G.1 Draw a figure's line(s) of symmetry and/or center of symmetry I M
G.G.2 Distinguish between a definition, theorem and a postulate M
G.G.2 Write a conditional, biconditional, converse and contrapositive M
G.G.2 Apply the properties of conditional statements when using conjectures M
G.G.3 Calculate the slope of a line or line segment given 2 coordinates M
G.G.10 Determine the range of lengths of the side of a triangle given 2 sides M
G.G.10 Determine if a length is possible for the third side of a triangle given 2 sides M
G.G.10 Given three lengths, determine if a triangle could be made with them M
G.G.10 Determine the order of length of sides of a triangle given the angles M
G.G.10 Define: x-axis, y-axis, the angles of triangle given the lengths of sides
Determine the order ofintercept, line,ahorizontal, vertical, oblique, slope, rate of M
G.G.11 (10.P.2) change M
G.G.11 (10.P.2) Plot a point on the coordinate plane M
Geometry Page 11 of 19 PD 9/16/05
Quarter 1
Identify a line as horizontal, vertical or oblique (increasing or decreasing) from its
G.G.11 (10.P.2) graph M
Identify a line as horizontal, vertical or oblique (increasing or decreasing) from its
G.G.11 (10.P.2) M
equation
G.G.11 (10.P.2) Calculate the slope of a line from two points using The Slope Formula M
Determine the slope of a line from an equation (in Slope-Intercept Form or Standard
G.G.11 (10.P.2) M
Form)
G.G.11 (10.P.2) Determine the slope of a line from its graph M
G.G.11 (10.P.2) Identify the x and y - intercepts from a graph M
Identify the x and y - intercepts from an equation (in Slope-Intercept Form or Standard
G.G.11 (10.P.2) M
Form)
G.G.11 (10.P.2) Given a graph, write the equation of a line in Slope - Intercept Form M
G.G.11 (10.P.2) Given a graph, write the equation of a line in Standard Form M
Write the equation of a line given one point on the line and the slope, using Point-
G.G.11 (10.P.2) M
Slope Form
G.G.11 (10.P.2) Write the equation of a line given two points, using Point-Slope form M
G.G.11 (10.P.2) Translate between all forms of equations M
G.G.11 (10.P.2) Define: positive slope, negative slope, zero slope and undefined (no) slope M
Classify the slope of a line as positive, negative, zero or undefined given a graph of the
G.G.11 (10.P.2) M
line
Classify the slope of a line as positive, negative, zero or undefined given the equation
G.G.11 (10.P.2) M
of the line
G.G.11 (10.P.2) Identify a line as horizontal, vertical, oblique (increasing or decreasing) from its slope M
G.G12 (10.G.7) Calculate the slope of a line or line segment given 2 coordinates M
G.G.17 (10.G.11) Define: network, node, odd node, even node, traversable M
G.G.17 (10.G.11) Determine the type of nodes in a network M
G.G.17 (10.G.11) Determine if a network is traversable M
G.G.17 (10.G.11) Identify starting point and ending point on a traversable network. M
Identify the path to get from the starting point to the ending point of a traversable
G.G.17 (10.G.11) M
network
Model a real world situation with a network and solve a related problem (e.g. bus
G.G.17 (10.G.11) M
routes)
Geometry Page 12 of 19 PD 9/16/05
Quarter 2
Benchmark Mastery Skills
Geometry - Quarter 2
Standard Q1 Q2 Q3 Q4
Note: The parentheses at the end of a learning standard contain the code number(s) for the corresponding standard(s) in the two-year grade spans.
G.G.1 Define: trapezoid, isosceles trapezoid, parallelogram, rectangle, kites, rhombus, square M
G.G.1 Distinguish between all types of quadrilaterals M
G.G.1 Show how quadrilaterals are related (e.g.. Use the Quadrilateral Hierarchy) M
G.G.1 Apply properties of diagonals in various quadrilateral M
G.G.1 Define: reflection symmetry, rotational symmetry I M
G.G.1 Determine a figure's type of symmetry I M
G.G.1 Draw a figure's line(s) of symmetry and/or center of symmetry I M
G.G.2 Prove two lines are parallel M
G.G.2 Prove two lines are perpendicular M
G.G.3 Calculate the distance between two coordinates M
G.G.3 Calculate the midpoint of a line segment given the coordinates of the endpoints M
Prove two lines are parallel, perpendicular or non-perpendicular intersecting lines by
G.G.3 M
using slopes
G.G.3 Define: congruent M
G.G.3 Prove segments are congruent by using the distance formula M
G.G.3 Prove a segment has been bisected by using the midpoint or distance formula M
Prove a triangle is equilateral, isosceles or right by using the distance formula and/or
G.G.3 M
slopes
Prove a quadrilateral is a trapezoid, isosceles trapezoid, parallelogram, kite, rhombus,
G.G.3 M
square or rectangle by using the distance formula and/or slopes
Define: complementary, supplementary, linear pair, vertical angles, parallel lines,
G.G.6 transversal, alternate interior angles (AIA), alternate exterior angles (AEA), M
corresponding angles
Calculate angle measures in problems involving complementary and supplementary
G.G.6 M
angles
G.G.6 Use the Linear Pair Theorem to calculate angle measures in a linear pair M
G.G.6 Use the Vertical Angle Theorem to calculate the measures of vertical angles M
Calculate a variety of angle measures (AIA, AEA, corresponding angles) when two
G.G.6 M
parallel lines are cut by a transversal
Geometry Page 13 of 19 PD 9/16/05
Quarter 2
Given angle measures (AIA, AEA, corresponding angles), determine if two lines are
G.G.6 M
parallel
G.G.7 (10.G.5) Use the Triangle Sum Property to find missing angles in a triangle M
Given two legs of a right triangle, calculate the length of the hypotenuse using the
G.G.7 (10.G.5) M
Pythagorean Theorem
Given one leg and the hypotenuse of a right triangle, calculate the length of the other
G.G.7 (10.G.5) M
leg using The Pythagorean Theorem
Given the length of one non-base side of an isosceles triangle, find the length of the
G.G.8 (10.G.6) M
other non-base side
G.G.8 (10.G.6) Use the Isosceles Base Angles Theorem to find base angles in an isosceles triangle M
G.G.8 (10.G.6) Find the lengths of sides in an equilateral triangle M
G.G.8 (10.G.6) Find the measures of angles in an equilateral triangle M
G.G.8 (10.G.6) Find the measures of angles in a right triangle M
Given two legs of a right triangle, calculate the length of the hypotenuse using the
G.G.8 (10.G.6) M
Pythagorean Theorem
Given one leg and the hypotenuse of a right triangle, calculate the length of the other
G.G.8 (10.G.6) M
leg using The Pythagorean Theorem
G.G12 (10.G.7) Calculate the distance between two coordinates M
G.G12 (10.G.7) Calculate the length of a line segment using the distance formula M
G.G12 (10.G.7) Calculate the midpoint of a line segment given the coordinates of the endpoints M
G.G12 (10.G.7) Apply the distance formula to solve a word problem M
G.G12 (10.G.7) Apply the midpoint formula to solve a word problem M
G.G12 (10.G.7) Apply the slope formula to solve a word problem M
G.G.13 (10.G.8) Define the relationship between the slopes of parallel lines M
G.G.13 (10.G.8) Write the equation of a line parallel to a given line through a given point M
G.G.13 (10.G.8) Determine if two lines are parallel given their slopes M
G.G.13 (10.G.8) Determine if two lines are parallel given their equations M
G.G.13 (10.G.8) Define the relationship between the slopes of perpendicular lines M
G.G.13 (10.G.8) Write the equation of a line perpendicular to a given line through a given point M
G.G.13 (10.G.8) Determine if two lines are perpendicular given their equations M
G.G.13 (10.G.8) Determine if two lines are perpendicular given their slopes M
Define: transformation, translation, reflection, rotation, scale/size change, scale factor,
G.G.15 (10.G.9) M
magnitude, isometry, preimage, image, orientation, vector
Use proper notation for reflections over a given line, multiple reflections, rotations,
G.G.15 (10.G.9) M
scale/size changes and vectors
Geometry Page 14 of 19 PD 9/16/05
Quarter 2
G.G.15 (10.G.9) Determine the orientation of a given figure M
G.G.15 (10.G.9) Reflect a point over a given line M
G.G.15 (10.G.9) Reflect a figure over a given line M
G.G.15 (10.G.9) Reflect a point over more than one line M
G.G.15 (10.G.9) Reflect a figure over more than one line (include both parallel and intersecting lines) M
G.G.15 (10.G.9) Rotate a point about a given point a given magnitude M
G.G.15 (10.G.9) Rotate a figure about a given point a given magnitude M
G.G.15 (10.G.9) Translate a point using reflections and using vectors M
G.G.15 (10.G.9) Translate a figure using reflections and using vectors M
G.G.15 (10.G.9) Given a preimage and a rotated image, determine the magnitude of the rotation M
G.G.15 (10.G.9) Given a preimage and a translated image, determine the magnitude of the translation M
G.G.15 (10.G.9) Given a preimage and a reflected image, find the line of reflection M
G.G.15 (10.G.9) Scale/Size change a figure on the coordinate plane M
G.G.15 (10.G.9) Given a preimage and a scale/size changed image, determine the scale change factor M
G.G.15 (10.G.9) Determine if two figures have the same orientation M
G.G.15 (10.G.9) Determine if a transformation is an isometry M
Given an image and a preimage, determine the type of transformation that has been
G.G.15 (10.G.9) M
applied
G.G.18 (12.G.3) Define: vector, horizontal component, vertical component M
G.G.18 (12.G.3) Use vectors to translate points and figures M
G.G.18 (12.G.3) Given a completed translation, identify the vector used M
G.G.18 (12.G.3) Add vectors symbolically M
G.G.18 (12.G.3) Add vectors pictorially M
G.G.18 (12.G.3) Multiply a vector by a scalar symbolically M
G.G.18 (12.G.3) Multiply a vector by a scalar pictorially M
G.M.1 (10.M.1) Calculate the perimeter of any triangle I M
G.M.1 (10.M.1) Calculate the perimeter of any quadrilateral I M
G.M.1 (10.M.1) Calculate the perimeter of any regular polygon I M
G.M.1 (10.M.1) Calculate the perimeter of a basic non-regular polygon (e.g.. pentagons, octagons, etc.) I M
G.M.1 (10.M.1) Calculate the circumference of a circle I M
G.M.1 (10.M.1) Given the perimeter of a figure, determine the length of missing sides I M
G.M.1 (10.M.1) Given the circumference of a circle, calculate the length of the radius (or diameter) I M
Geometry Page 15 of 19 PD 9/16/05
Q3 Geometry
Benchmark Mastery Skills
Geometry - Quarter 3
Standard Q1 Q2 Q3 Q4
Note: The parentheses at the end of a learning standard contain the code number(s) for the corresponding standard(s) in the two-year grade spans.
G.G.2 Prove triangles are congruent M
G.G.2 Prove triangles are similar M
Prove a figure is a specific type of polygon (e.g.. Prove a figure is a rhombus by
G.G.2 M
showing all four sides are congruent)
Use a variety of techniques to prove including inductive reasoning, deductive
G.G.2 M
reasoning and counterexample or contradiction.
G.G.4 Draw congruent figures using a compass, straightedge, protractor or computer software M
G.G.4 Draw similar figures using a compass, straightedge, protractor or computer software M
G.G.4 Construct geometric figures using only a compass and straightedge M
G.G.4 Use appropriate methods of construction and explain their use M
G.G.5 (10.G.4) Define: similar figures, proportion M
G.G.5 (10.G.4) Solve a proportion using the Means Extremes Theorem M
G.G.5 (10.G.4) Find missing pieces of similar figures by using a proportion M
G.G.5 (10.G.4) Use the properties of congruence to find missing pieces in two congruent figures M
G.M.1 (10.M.1) Calculate the perimeter of any triangle I M
G.M.1 (10.M.1) Calculate the perimeter of any quadrilateral I M
G.M.1 (10.M.1) Calculate the perimeter of any regular polygon I M
G.M.1 (10.M.1) Calculate the perimeter of a basic non-regular polygon (e.g.. pentagons, octagons, etc.) I M
G.M.1 (10.M.1) Calculate the circumference of a circle I M
G.M.1 (10.M.1) Given the perimeter of a figure, determine the length of missing sides I M
G.M.1 (10.M.1) Given the circumference of a circle, calculate the length of the radius (or diameter) I M
G.M.1 (10.M.1) Calculate the area of any triangle M
G.M.1 (10.M.1) Calculate the area of any trapezoid, parallelogram, rhombus, kite, rectangle or square M
G.M.1 (10.M.1) Calculate the area of a regular polygon by breaking it up M
G.M.1 (10.M.1) Calculate the area of any irregular polygon by breaking it up M
G.M.1 (10.M.1) Calculate the area of a circle M
G.M.1 (10.M.1) Given the area of a figure, calculate the length of a particular side M
G.M.1 (10.M.1) Given the area of a circle, calculate the length of the radius (or diameter) M
Q3 Geometry
Given the measurement of a 2-D object, calculate another measure (e.g.. Find the
G.M.1 (10.M.1) M
perimeter of a square given its area)
G.M.1 (10.M.1) Solve a word problem by calculating perimeters, circumferences or areas M
G.M.2 (10.M.2) Define: lateral area, surface area, volume, base, edge, face M
Identify and label (i.e. base, edge, radius, etc.) prisms, pyramids, cylinders, cones and
G.M.2 (10.M.2) M
spheres
Identify the difference between lateral area and surface area or prisms, pyramids,
G.M.2 (10.M.2) M
cylinders and cones
G.M.2 (10.M.2) Calculate the lateral area of prisms, pyramids, cylinders and cones M
G.M.2 (10.M.2) Calculate the surface area of prisms, pyramids, cylinders, cones and spheres M
G.M.2 (10.M.2) Calculate the volume of prisms, pyramids, cylinders, cones and spheres M
Given the measurement of a 3-D object, calculate another measure (e.g.. Find the
G.M.2 (10.M.2) M
lateral area of a cylinder given its volume and height)
Solve word problems by calculating the lateral area of prisms, pyramids, cylinders and
G.M.2 (10.M.2) M
cones
Solve word problems by calculating the surface area of prisms, pyramids, cylinders,
G.M.2 (10.M.2) M
cones and spheres
Solve word problems by calculating the volume of prisms, pyramids, cylinders, cones
G.M.2 (10.M.2) M
and spheres
G.M.3 (10.M.3) Determine how changing one attribute of an object affects its perimeter M
G.M.3 (10.M.3) Determine how changing one attribute of an object affects its area M
G.M.3 (10.M.3) Determine how changing one attribute of an object affects its lateral area M
G.M.3 (10.M.3) Determine how changing one attribute of an object affects its surface area M
G.M.3 (10.M.3) Determine how changing one attribute of an object affects its volume M
G.M.4 (10.M.4) Describe the effect of measurement errors when calculating perimeter, area and M
G.M.4 (10.M.4) volume the effect of rounding when calculating perimeter, area and volume
Describe M
G.M.5 (12.M.2) Convert units in the metric system (e.g. cm to m) M
G.M.5 (12.M.2) Convert units in the standard system (e.g. ft to mi) M
G.M.5 (12.M.2) Convert between two measurement systems (e.g.. centimeters to inches) M
G.M.5 (12.M.2) Use appropriate units in measurements (ex. volume uses cubic units) M
Determine whether given units in a problem make sense or need to be converted (ex.
G.M.5 (12.M.2) M
length given in inches, width given in feet, calculate the area)
Geometry Q4
Benchmark Mastery Skills
Geometry - Quarter 4
Standard Q1 Q2 Q3 Q4
Note: The parentheses at the end of a learning standard contain the code number(s) for the corresponding standard(s) in the two-year grade spans.
Define: radii, chord, tangent, secant, inscribed angle, exterior angle, central angle,
G.G.6 M
major arc, minor arc
G.G.6 Given angle measures (inscribed, exterior, central), calculate the length of an arc M
Given the length of an arc, calculate a variety of angle measures (inscribed, exterior,
G.G.6 M
central)
G.G.6 Calculate lengths of radii, chords, tangents and secants M
G.G.6 Calculate parts of chords, tangents and secants when they intersect M
Given the length of one side of a 45º–45º–90º triangle, find the lengths of the
G.G.8 (10.G.6) M
remaining sides
Given the length of one side of a 30º–60º–90º triangle, find the lengths of the
G.G.8 (10.G.6) M
remaining sides
G.G.9 Label the sides of a right triangle appropriately (opposite, adjacent, hypotenuse) M
G.G.9 Define: sine, cosine, and tangent of an acute angle M
G.G.9 Use SOHCAHTOA or another device to remember the ratios M
G.G.9 Create the sine, cosine or tangent ratio given a right triangle M
G.G.9 Find the sine, cosine or tangent ratio using a calculator M
G.G.9 Use inverse ratios to find angle measure corresponding to a given trig ratio value M
G.G.9 Solve for missing sides in a right triangle using the appropriate ratio M
G.G.9 Solve for missing angles in a right triangle using the appropriate ratio M
G.G.9 Model and solve real world problems using the appropriate trig ratio M
Given the center and radius (or diameter) of a circle, write an equation representing the
G.G.14
circle M
G.G.14 Given an equation of a circle in standard form, determine the center and radius M
G.G.14 Given an equation of a circle in standard form, graph the circle M
G.G.14 Given a graph of a circle, determine the center and radius (or diameter) of the circle M
G.G.14 Given a graph of a circle, write an equation in standard form to represent the circle M
G.G.16 (10.G.10) Define: net, cross section, projection M
G.G.16 (10.G.10) Given a solid object, draw its net M
G.G.16 (10.G.10) Given a net, determine the solid object it represents M
Geometry Q4
G.G.16 (10.G.10) Determine if a solid object can be made from a given net M
G.G.16 (10.G.10) Determine the view of a solid object from above, from the left and from the right M
Given a projection and a solid object, determine if it is a view from above, from the
G.G.16 (10.G.10) M
left or from the right
G.G.16 (10.G.10) Given a projection, determine if it represents a particular solid object M
Determine the cross section of a plane and a given solid. Orient the intersecting plane
G.G.16 (10.G.10) M
Determine the orientation of the perpendicular to which of the the given obliquely
parallel to the base of the object, intersecting planethe basecreates object andcross
G.G.16 (10.G.10) section M
Determine if a given cross section can be made from the intersection of a plane and a
G.G.16 (10.G.10) M
solid object