Syllabus Geometry
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to:
First Nine Weeks Recognize and use the symbols of [SOL .5] Solve for missing lengths in geometric
formal logic, which include →,↔, ~, , figures, using properties of 45°-45°-
[SOL .3] ∧ , and ∨. Order the sides of a triangle by their 90° triangles.
lengths when given the measures of Solve for missing lengths in geometric
Find the coordinates of the midpoint of [SOL.2] the angles. figures, using properties of 30°-60°-
a segment, using the midpoint formula. Given the lengths of three segments, 90° triangles.
Use a formula to find the slope of a Use algebraic and coordinate methods determine whether a triangle could be Solve problems involving right
line. as well as deductive proofs to verify formed. triangles, using sine, cosine, and
Apply the distance formula to find the whether two lines are parallel. Order the angles of a triangle by their tangent ratios.
length of a line segment when given Solve problems by using the measures when given the lengths of Solve real-world problems, using right
the coordinates of the endpoints. relationships between pairs of angles the sides. triangle trigonometry and properties
Compare the slopes to determine formed by the intersection of two Given the lengths of two sides of a of right triangles.
whether two lines are parallel, parallel lines and a transversal triangle, determine the range in which
perpendicular, or neither. including corresponding angles, the length of the third side must lie. [SOL .10]
alternate interior angles, alternate Solve real-world problems given
[SOL .1] exterior angles, and same-side information about the lengths of sides Identify tessellations in art,
(consecutive) interior angles. and/or measures of angles in construction, and nature.
Identify the converse, inverse, and Solve real-world problems involving triangles. Solve real-world problems involving
contrapositive of a conditional intersecting and parallel lines in a the measures of interior and exterior
statement. plane. [SOL .7] angles of polygons.
Translate verbal arguments into Use coordinate methods, such as the Find the sum of the measures of the
symbolic form, such as Second Nine Weeks distance formula, to prove two interior and exterior angles of a
(p → q) and (~p → ~q). triangles are similar. Use algebraic convex polygon.
Determine the validity of a logical methods to prove that triangles are Find the measure of each interior and
argument. [SOL .6] similar. exterior angle of a regular polygon.
Use valid forms of deductive Use definitions, postulates, and Find the number of sides of a regular
reasoning, including the law of Use definitions, postulates, and theorems to prove triangles similar. polygon, given the measures of
syllogism, the law of the theorems to prove triangles interior or exterior angles of the
contrapositive, the law of detachment, congruent. Third Nine Weeks polygon.
and counterexamples Use coordinate methods, such as the
Select and use various types of distance formula and the slope [SOL .8]
reasoning and methods of proof, as formula, to prove two triangles are [SOL .9]
appropriate. congruent. Determine whether a triangle formed
Use Venn diagrams to represent set Use algebraic methods to prove two with three given lengths is a right Solve problems, including real-world
relationships, such as intersection and triangles are congruent. triangle. problems, using the properties
union. specific to parallelograms, rectangles,
Interpret Venn diagrams.
Syllabus Geometry
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to:
rhombi, squares, isosceles trapezoids, Calculate the area of a sector and the – the perpendicular bisector Describe how changes in one or more
and trapezoids. length of an arc of a circle, using of a line segment; dimensions affect other derived
Prove that quadrilaterals have specific proportions. – a perpendicular to a given measures (perimeter, area, total
properties, using coordinate and Solve real-world problems associated line from a point not on the surface area, and volume) of an
algebraic methods, such as the with circles, using properties of line; object.
distance formula, slope, and midpoint angles, lines, and arcs. – a perpendicular to a given Solve real-world problems involving
formula. Verify properties of circles, using line at a point on the line; measured attributes of similar objects
Prove the characteristics of deductive reasoning, algebraic, and – the bisector of a given Describe how changes in one or more
quadrilaterals, using deductive coordinate methods. angle; measures (perimeter, area, total
reasoning, algebraic, and coordinate – an angle congruent to a surface area, and volume) affect other
methods. [SOL .12] given angle; and measures of an object.
– a line parallel to a given line
[SOL .3] Identify the center, radius, and through a point not on the
diameter of a circle from a given given line.
• Determine whether a figure has point standard equation.
symmetry, line symmetry, both, or Use the distance formula to find the [SOL .13]
neither. radius of a circle.
• Given an image and preimage, identify Given the coordinates of the center Find the total surface area of
the transformation that has and radius of the circle, identify a cylinders, prisms, pyramids, cones,
• taken place as a reflection, rotation, point on the circle. and spheres, using the appropriate
dilation, or translation. Given the equation of a circle in formulas.
standard form, identify the Calculate the volume of cylinders, Contact Information:
Fourth Nine Weeks coordinates of the center and find the prisms, pyramids, cones, and spheres,
radius of the circle. using the appropriate formulas.
cdrury@pgs.k12.va.us
[SOL .11] Given the coordinates of the endpoints Solve problems, including real-world
of a diameter, find the equation of the problems, involving total
Find lengths, angle measures, and arc surface area and volume of cylinders, School Telephone:
circle.
measures associated with Given the coordinates of the center prisms, pyramids, cones, and spheres
– two intersecting chords; and a point on the circle, find the as well as combinations of three- 804-733-2748
– two intersecting secants equation of the circle. dimensional figures.
–an intersecting secant and tangent Calculators may be used to find
– two intersecting tangents; [SOL .4] decimal approximations for results.
and [SOL.14]
– central and inscribed Construct and justify the Compare ratios between side lengths,
angles. constructions of perimeters, areas, and volumes, given
– a line segment congruent to two similar figures.
a given line segment;