Geometry SOL Sheet

Geometry SOL Sheet Construct and judge the validity of a logical argument consisting of a set of premises and a conclusion: 1) identifying the converse, inverse, and contrapositive of a conditional statement; 2) translate a short verbal argument into symbols; 3) Diagram arguments involving quantifiers (all, no, none, some) using Venn diagrams; 4) use valid forms of deductive reasoning, including the law of syllogism. Enabling Objectives:            To identify and order the parts of a conditional statement (hypothesis / conclusion). To write a conditional statement in proper form using “if-then”. To understand the process of assigning variables to unknowns. To recognize symbols: ~, p, q,,,, Be able to translate verbal arguments into symbols. Be able to distinguish between conditional, converse, inverse, and contrapositive. Draw and identify basic parts of a Venn diagram. Understand the difference in the quantifiers (all, some, etc.) when using Venn diagrams. Understand the difference between validity and truth. Understand the different valid forms of deductive reasoning – law of detachment and syllogisms. Introduce the transitive property as it applies to syllogisms. G.1 Geometry SOL G.2 G.2 Use pictorial representations, including computer software and coordinate methods to solve problems involving symmetry and transformation. 1) use formulas for finding distance, midpoint, and slope; 2) determine whether a figure is symmetric with respect to a line or a point; and 3) determine whether a figure has been translated, reflected, or rotated.                 To identify, describe and draw models of points, lines, planes, segments, rays, intersecting lines and planes and perpendicular lines and planes [ Glencoe 1.2 p 12 ] To use the concept of collinear, points between points, angle measure, and distance measure. [Glencoe 1.1 p 6 ; 1.4 p 28 To understand the difference between AB, AB, AB, and AB [ Glencoe 1.2 p 12 ] To know that measure of segments is always positive. To find the distance between two points on the number line using the Segment Addition Postulate. [ Glencoe 1.4 p 29 ] To find the distance between two points on the coordinate plane using the distance formula [ Glencoe 1.4 p 31] To find the midpoint of a segment on the number line or coordinate plane [ Glencoe 1.5 p 35] To find the slope of a line in the coordinate plane [ Glencoe 3.3 p 138 ] To define line of symmetry and point of symmetry [ Glencoe 13.5 p 722 ] To use the symmetric property to determine if a figure is symmetric with respect to a line or a point [ Glencoe 13.4 p 722] To identify figures where a line of reflection can be drawn so that one side is a reflected image of the other side. To identify a point of symmetry by showing it is the midpoint of all segments that pass through it and the endpoints are on the figures. To define translation, reflection, and rotation. [ Glencoe 10.2A p 522; 13.4 p 715; 13.5 p 722; 13.6 p 731; 13.7 p 739 ] To understand the difference between translation (slide), reflection (flip), and rotation (turn) of a figure. To identify types of transformations by using pre-image and image points. To determine whether a figure has been translated, reflected, or rotated. To identify and describe symmetrical two-dimension figures, using tracing procedures. To identify the ordered pair of a point in the first quadrant of a coordinate plane. To identify applications of transformations such as tiling, fabric design, art, and scaling. To solve an algebraic equation. To estimate square roots. To understand absolute value. To use the laws of exponents in solving an algebraic equation To determine the slope of a line when given the graph of the line, the equation of the line, or two points on the line using the slope formula. To graph ordered pairs on a coordinate plane. [ Glencoe 1.1 p 6 ] To identify the vertical (rise) change and the horizontal (run) change between two points on the coordinate plane. Grade 3 Grade 5 Grade 8 Algebra I Geometry SOL G.3 G3 Solve practical problems involving complementary, supplementary, and congruent angles that include vertical angles, angles formed when parallel lines are cut by a transversal, and angles in polygons.               To identify, draw, measure, and classify angles as right, acute, straight, or obtuse [ Glencoe 1.6 p 44 ] To identify and use adjacent, vertical, complementary, supplementary, and linear pairs of angles. [ Glencoe 1.7 p 53 ] To define congruency. [ Glencoe 1.4 p 31 ] To determine the bisector of an angle. [ Glencoe 1.6 p 48 ] To determine the measures of angles using the angle Addition Postulate. [ Glencoe 1.6 p 46 ] To solve practical problems involving complementary, supplementary, and vertical angles. To define transversal and understand the concept of parallel lines. [ Glencoe 3.1 p 126; 4.1 p 180 ] To use properties of parallel lines to determine angle measures. [ Glencoe 3.2 p 131 ] To solve practical problems involving parallel lines cut by a transversal. To identify and name polygons. [ Glencoe 10.1 p 514 ] To determine if the polygon is concave or convex or if the polygon is regular. [ Glencoe 10.1 p 514 ] To find the sum of of the measures of interior and exterior angles of convex polygons. [ Glencoe 10.1 p 516] To find the sum of the measures of interior and exterior angles of regular polygons. [ Glencoe 10.1 p 516 ] To solve problems involving angle measures of polygons. [ Glencoe 10.1 p 519 ] To identify and draw representations of line segments and angles using a ruler straightedge. To identify lines that illustrate intersection, parallelism, and perpendicularity. To classify angles as right, acute, or obtuse. To draw and measure right, acute, and obtuse angles using appropriate tools. To determine congruence of segments, angles, and polygons. To draw and identify the following polygons; pentagon, hexagon, heptagon, octagon, nonagon, and decagon. To classify angles as acute, right, obtuse, congruent, complementary, or supplementary. Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Pre-Algebra Geometry SOL sheet G.4 Use the relationships between angles formed by two lines cut by a transversal to determine if two lines are parallel: verify that the lines are parallel using algebraic and coordinate methods as well as deductive proofs. Enabling Objectives:     Review definitions of parallel and transversal lines. Identify interior angles, exterior angles, alternate interior/exterior angles, corresponding angles, and same-side interior/exterior angles (consecutive interior/exterior angles) Now the relationship between special angles and parallel lines. Using the definitions of complementary and supplementary angles prove lines are parallel ( i.e. through proofs ) Apply postulates and theorems relating to parallel lines.  Gemoetry SOL Sheet G.5 Identify congruence and similarity relationships between triangles; given information in the form of a figure or statement, prove two triangles are congruent or similar using algebraic/coordinate methods and deductive proofs. Enabling Objectives:           Identify and name parts of triangles – including a right triangle, an isosceles triangle and an equilateral triangle. Define congruent triangles and their corresponding parts. Use tic-marks to mark congruencies on diagrams. Write a triangle congruency statement – matching corresponding parts in correct order. Prove two triangles congruent by deductive proofs – using diagrams and statements. Methods: SAS, SSS, ASA, AAS, HL, HA, LA, LL Prove two triangles congruent by coordinate geometry. Define similar triangles and the symbol for similarity. Determine by statement or diagram if two figures are similar. Write a similarity statement – matching corresponding parts. Prove two triangles similar by AA, SS, and SAS similarity. Apply theorems and postulates concerning similar triangles to find missing angle and side measures. Prove two triangles similar by using coordinate geometry.  Geometry Sheet G.6 Given information concerning the lengths of sides and/or measures of angles, apply the triangle inequality properties to 1) determine whether a triangle exists 2) order sides and angles ( concepts presented in practical situations). Enabling Objectives:         Know the definition of a triangle. Identify the parts of a triangle. Classify triangles by side and angle measures. Apply the Triangle Sum Theorem. Understand >, <, and =. Apply the Triangle Inequality Theorem. Understand the meaning of opposite sides and angles in triangles. Understand ordering from least to greatest and greatest to least. Geometry SOL Sheet G.7 Solve practical problems involving right triangles by using the Pythagorean Theorem and its converse, properties of special right triangles, and right triangle trigonometry (use calculators to solve or find decimal approximations). Enabling Objectives:       Understand the relationships between the sides and angles of a right triangle. Use the Pythagorean Theorem and its converse to solve right triangle problems. Use the properties of the 30-60-90 and 45-45-90 triangles to find missing side measures. Identify and label parts of a right triangle using the three most common trigonometric ratios – sine, cosine, and tangent. (use mnemonic – SOHCAHTOA) Use a calculator to find values of trig ratios or measures of angles. Use trigonometry to solve practical problems. Geometry SOL G.8 G.8 Identify properties of quadrilaterals involving opposite sides and angles, consecutive sides and angles, and diagonals; prove properties using algebraic, coordinate, and deductive proofs; use properties to solve practical problems. Enabling Objectives:              To use the concepts of angle measure, parallel lines, and perpendicular lines. To use the concepts of congruency, slop, midpoint, and distance formula. To define a quadrilateral, parallelogram, rectangle, square, rhombus, and trapezoid. [ Glencoe 6.1 p 291; 6.3 p 306; 6.4 p 313; 6.5 p 321 ] To recognize the difference between a side and a diagonal of a quadrilateral. [ Glencoe 6.1 p 293 ] To recognize and apply the properties of a parallelogram [ Glencoe 6.1 p 291 ] To recognize and apply the conditions that insure a quadrilateral is a parallelogram. [ Glencoe 6.2 p 298] To recognize and apply the properties of rectangles [ Glencoe 6.3 p 306 ] To recognize and apply the properties of squares and rhombi [ Glencoe 6.4 p 313 ] To identify the parts of a trapezoid (legs, bases, median). [ Glencoe 6.5 p 332 ] To calculate the median of a trapezoid using the formula. [ Glencoe 6.5 p 323 ] To recognize and apply the properties of trapezoids and isosceles trapezoids. [ Glencoe 6.5 p 321 ] To compare and contrast parallelograms, rectangles, squares, and rhombi. To use the properties of quadrilaterals to solve practical problems. To identify and construct plane geometric figures. To identify models of plane geometric figures To compare the size and shape of plane geometric figures. To draw and describe squares and rectangles. To compare and contrast plane and solid geometric figures. To compare and contrast quadrilaterals. Kindergarten Grade 1 Grade 2 Grade 7 Geometry SOL Sheet G.9 Use measures of interior and exterior angles of polygons to solve problems. Make connections to art, construction, and nature with tessellation & tiling. Enabling Objectives:         Identify concave and convex polygons. Identify interior and exterior angles of a polygon. Classify polygons by the number of its sides. Recall the meanings of equilateral an equiangular. Define regular polygon. Introduce the formula for finding the sum of the measures of the interior angles of a convex polygon with n sides: 180(n –2) Understand basic constructions, tessellation, and tiling. Make connections by using Art (i.e. quilt pieces or textile designs), construction (i.e. aerial view of the Pentagon), and nature with tessellation and tiling (i.e. sugar crystals). Geometry SOL sheet G.10 Investigate and use the properties of angles, arcs, chords, tangents, and secants to solve problems involving circles. Problems will include finding the area of a sector and applications of architecture, art, and construction. Enabling Objectives:          Define and identify the parts of a circle. Use the appropriate notation to name the parts of a circle. Draw and label parts of a circle. To apply the theorems and postulates of chords, radii, tangents and secants to find missing measurements. To apply the theorems and postulates of circles to find the measure of central angles, inscribed angles, major, and minor arcs. Find the circumference and area of a circle. Define arclength, sector, and segment of a circle and find their measures. To know and write the equation of a circle. To be able to identify the center and radius of a circle given its equation. Geometry SOL Sheet G.11 Construct, using a compass and straightedge, a line segment congruent to a given line segment, the bisector of a line segment a perpendicular to a given line from a point not on the line, a perpendicular to a given line AT a point on the line, the bisector of a given angle, and an angle congruent to a given angle. Enabling Objectives:      Know the difference between drawing and constructing. Identify a compass and a straightedge along with the proper usage of each. Remind students of the definition of congruence. Define bisector of a line and an angle, and perpendicular. Know the symbols for lines, segments, angles, and perpendicular. Geometry SOL Sheet G.12 Make a model of a 3-dimensional figure from a 2-dimensional drawing; make a 2-dimensional drawing of a 3-dimensional object. Models and representations will include scale drawings, perspective drawings, blueprints, or computer simulations. Enabling Objectives:    Know the difference between 2-dimensional and 3-dimensional. Define scale drawing, perspective drawing, blueprints, and computer simulations (if able, show an example of each). Compare and contrast plane and solid figures. Geometry SOL Sheet G.13 Use formulas for surface area and volume of 3-dimensional objects to solve practical problems. Calculators will be used for decimal approximations of results. Enabling Objectives:     Review the formulas for finding area and perimeter of plane figures. (use formula sheets.) Identify and label the parts of a 3-dimensional figure (prism, pyramid, cylinder, cone, and sphere). Use formulas to calculate the lateral area, surface area, and volume of 3-dimensional figures. Use a calculator to determine decimal approximations of areas and volumes of figures. Geometry SOL Sheet G.14 Given similar geometric objects, use proportional reasoning to solve practical problems; investigate relationships between linear, square, and cubic measures; describe how changes in one of the measures affect the others. Enabling Objectives:    Review writing ratios and solving proportions. Use proportional reasoning to compare the perimeters, areas and volume of similar 3-dimensional figures. Solve practical problems involving similar geometric figures. Geometry SOL G.15 G.15 Draw a system of vectors and find the resultant graphically, write the components of a vector as a column matrix, and find the resultant by matrix addition; and solve practical problems using a system of vectors. Enabling objectives:  To define a column matrix  To define matrix addition.  To use the concepts of signed numbers, parallel lines, slope, matrix addition, scalar multiplication, distance formula, and estimation of square roots.  To define vector and magnitude [ Glencoe 12.5 p 673 ]  To understand the notation for a vector. [ Glencoe 12.5 p 673 ]  To find the magnitude and direction of a vector. [ Glencoe 12.5 p 673 ]  To determine if two vectors are equal. [Glencoe 12.5 p 674 ]  To draw a system of vectors and find the resultant graphically. [ Glencoe 12.5 p675]  To write the components of a vector as a column matrix. [ Glencoe 12.5 p 676 ]  To find the resultant by matrix additions. [ Glencoe 12.5 p 676 ]  To perform operations with vectors. [ Glencoe 12.5 p 677 ]  To solve practical problems using a system of vectors.