Geometry Unit 2 Test , 3.8,
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1 Name: Class: Date: ID: A Geometry Unit 2 Test , 3.8, Short Answer - You are allowed to use your notes and calculator. No cell phones.good luck! 1. Line r is parallel to line t. Find m 5. The diagram is not to scale. 4. Find m Q. The diagram is not to scale. 2. Find the value of the variable if m Ä l, m 1 = 2x + 44 and m 5 = 5x The diagram is not to scale. 5. If c b and a Ä c, what is m 2? 6. Find the values of x, y, and z. The diagram is not to scale. 3. Find the values of x and y. The diagram is not to scale. 1
2 Name: ID: A 7. Find the value of x. The diagram is not to scale. 11. The sum of the measures of two exterior angles of a triangle is 255. What is the measure of the third exterior angle? 8. Find the value of the variable. The diagram is not to scale. 12. Use less than, equal to, or greater than to complete the statement. The measure of each exterior angle of a regular 7-gon is the measure of each exterior angle of a regular 5-gon. 13. Use less than, equal to, or greater than to complete the statement. The sum of the measures of the exterior angles of a regular 5-gon, one at each vertex, is the sum of the measures of the exterior angles of a regular 9-gon, one at each vertex. 9. How many sides does a regular polygon have if each exterior angle measures 20? 14. Find m A. The diagram is not to scale. 10. Find the missing angle measures. The diagram is not to scale. 15. A nonregular hexagon has five exterior angle measures of 55, 60, 69, 57, and 57. What is the measure of the interior angle adjacent to the sixth exterior angle? 2
3 Name: ID: A 16. Give the missing reasons in this proof of the Alternate Interior Angles Theorem. Given: l Ä n Prove: 4 6 Statments 1. l Ä n Reasons 1. Given a. b. c. 17. Find the values of the variables. Show your work and explain your steps. The diagram is not to scale. 18. Find the measures of an interior angle and an exterior angle of a regular polygon with 6 sides. 19. Explain how to tell whether a polygon is convex or concave. 3
4 Name: ID: A BONUS ( 1 pt each question) The hexagon GIKMPR and ΔFJN are regular. The dashed line segments form 30 angles. 20. Find the image of OQ after a rotation of 240 about point O. 25. BONUS (1 pt) Find the value of x for which l is parallel to m. The diagram is not to scale. 21. Find the image of point P after a rotation of 240 about point M. 22. Find the angle of rotation about O that maps JK to FG. 23. Find the angle of rotation about O that maps Q to F. 26. BONUS (1 pt) Find the value of k. The diagram is not to scale. 24. BONUS ( 1pt) m 1 = 6x and m 3 = 120. Find the value of x for p to be parallel to q. The diagram is not to scale. 4
5 ID: A Geometry Unit 2 Test , 3.8, Answer Section SHORT ANSWER 1. ANS: 135 PTS: 1 DIF: L2 REF: 3-1 Properties of Parallel Lines TOP: 3-1 Example 4 KEY: parallel lines alternate interior angles 2. ANS: 2 PTS: 1 DIF: L2 REF: 3-1 Properties of Parallel Lines TOP: 3-1 Example 5 KEY: corresponding angles parallel lines 3. ANS: x = 77, y = 57 PTS: 1 DIF: L2 REF: 3-1 Properties of Parallel Lines TOP: 3-1 Example 5 KEY: corresponding angles parallel lines 4. ANS: 60 PTS: 1 DIF: L3 REF: 3-1 Properties of Parallel Lines KEY: angle parallel lines transversal 5. ANS: 90 PTS: 1 DIF: L3 REF: 3-3 Parallel and Perpendicular Lines OBJ: Relating Parallel and Perpendicular Lines STA: CA GEOM 7.0 TOP: 3-3 Example 2 KEY: parallel lines perpendicular lines transversal 6. ANS: x = 86, y = 67, z = 94 PTS: 1 DIF: L2 REF: 3-4 Parallel Lines and the Triangle Angle-Sum Theorem OBJ: Finding Angle Measures in Triangles STA: CA GEOM 12.0 CA GEOM 13.0 TOP: 3-4 Example 1 KEY: triangle sum of angles of a triangle 1
6 ID: A 7. ANS: 33 PTS: 1 DIF: L2 REF: 3-4 Parallel Lines and the Triangle Angle-Sum Theorem OBJ: Using Exterior Angles of Triangles STA: CA GEOM 12.0 CA GEOM 13.0 TOP: 3-4 Example 3 KEY: triangle sum of angles of a triangle 8. ANS: 19 PTS: 1 DIF: L3 REF: 3-4 Parallel Lines and the Triangle Angle-Sum Theorem OBJ: Finding Angle Measures in Triangles STA: CA GEOM 12.0 CA GEOM 13.0 KEY: triangle sum of angles of a triangle vertical angles 9. ANS: 18 sides PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum Theorems TOP: 3-5 Example 3 KEY: sum of angles of a polygon 10. ANS: x = 114, y = 56 PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum Theorems TOP: 3-5 Example 4 KEY: exterior angle Polygon Angle-Sum Theorem 11. ANS: 105 PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum Theorems KEY: angle triangle exterior angle Polygon Angle-Sum Theorem 12. ANS: less than KEY: sum of angles of a polygon 13. ANS: equal to KEY: sum of angles of a polygon 14. ANS: 73 KEY: pentagon exterior angle sum of angles of a polygon 2
7 ID: A 15. ANS: 118 KEY: hexagon angle exterior angle 16. ANS: a. Corresponding angles. b. Vertical angles. c. Transitive Property. PTS: 1 DIF: L2 REF: 3-1 Properties of Parallel Lines TOP: 3-1 Example 3 KEY: alternate interior angles Alternate Interior Angles Theorem proof reasoning two-column proof multi-part question 17. ANS: [4] w = 180, so w = 59º. Since vertical angles are congruent, y = 59º. Since supplementary angles have measures with sum 180, x = v = 121º. z y = z = 180, so z = 53º. [3] small error leading to one incorrect answer [2] three correct answers, work shown [1] two correct answers, work shown PTS: 1 DIF: L3 REF: 3-4 Parallel Lines and the Triangle Angle-Sum Theorem OBJ: Using Exterior Angles of Triangles STA: CA GEOM 12.0 CA GEOM 13.0 KEY: Triangle Angle-Sum Theorem vertical angles supplementary angles extended response rubric-based question 18. ANS: m (interior) = 120 m (exterior) = 60 PTS: 1 DIF: L2 REF: 3-5 The Polygon Angle-Sum Theorems KEY: Polygon Exterior Angle-Sum Theorem exterior angle interior angle 19. ANS: A polygon is convex if the points of all the diagonals are inside or on the polygon. OBJ: Classifying Polygons STA: CA GEOM 12.0 CA GEOM 13.0 KEY: classifying polygons concave convex writing in math 20. ANS: OH PTS: 1 DIF: L2 REF: 9-3 Rotations OBJ: Drawing and identifying rotation images STA: CA GEOM 22.0 TOP: 9-3 Example 3 KEY: rotation degree of rotation image 3
8 ID: A 21. ANS: K PTS: 1 DIF: L2 REF: 9-3 Rotations OBJ: Drawing and identifying rotation images STA: CA GEOM 22.0 TOP: 9-3 Example 2 KEY: rotation degree of rotation image 22. ANS: 120 PTS: 1 DIF: L2 REF: 9-3 Rotations OBJ: Drawing and identifying rotation images STA: CA GEOM 22.0 TOP: 9-3 Example 3 KEY: rotation degree of rotation image 23. ANS: 300 PTS: 1 DIF: L2 REF: 9-3 Rotations OBJ: Drawing and identifying rotation images STA: CA GEOM 22.0 TOP: 9-3 Example 3 KEY: rotation degree of rotation image 24. ANS: 20 PTS: 1 DIF: L2 REF: 3-3 Parallel and Perpendicular Lines OBJ: Relating Parallel and Perpendicular Lines STA: CA GEOM 7.0 TOP: 3-3 Example 2 KEY: parallel lines 25. ANS: 28 PTS: 1 DIF: L4 REF: 3-2 Proving Lines Parallel OBJ: Using a Transversal STA: CA GEOM 2.0 CA GEOM 4.0 CA GEOM 7.0 TOP: 3-2 Example 2 KEY: parallel lines transversal 26. ANS: 73 PTS: 1 DIF: L2 REF: 3-4 Parallel Lines and the Triangle Angle-Sum Theorem OBJ: Finding Angle Measures in Triangles STA: CA GEOM 12.0 CA GEOM 13.0 TOP: 3-4 Example 1 KEY: triangle sum of angles of a triangle 4
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