Geometry Lucy Study Guide for Test #3 PDF

Geometry Online (Teaching Textbooks) First Quarter Seton Test 3 (Test includes material up to Lesson 21. Take after Lesson 21.) 1. (L15) Complementary angles are angles whose measures add up to _____ degrees. A. 180 B. 45 C. 360 D. 90 E. Not ap...

Geometry Online (Teaching Textbooks) First Quarter Seton Test 3 (Test includes material up to Lesson 21. Take after Lesson 21.) 1. (L15) Complementary angles are angles whose measures add up to _____ degrees. A. 180 B. 45 C. 360 D. 90 E. Not applicable 2. (L20) Is the following sentence true? If the exterior sides of a pair of adjacent angles are perpendicular, then the angles are equal. A. Yes B. No C. Depends on the exterior sides D. Either A or C E. None of the above 3. (L2) The following argument is a(n) _____ deduction: If two angles are supplementary to the same angle, then they are congruent. If ∠ A and ∠ B are supplementary to each other, then they are congruent. A. valid B. invalid C. Not enough data to determine D. Neither A nor B E. None of the above 4. (L4) The following argument is a(n) _____ deduction. Adjacent angles are angles that have the same vertex, share a common side, and have no interior points in common. Since ∠ 1 and ∠ 2 do not share a common side, they are not adjacent. A. valid B. invalid C. Not enough data to determine D. Neither A nor B E. None of the above  ⃗ bisects ∠ WXZ, m ∠ WXY = 4x – 1, and m ∠ YXZ = 2x + 15, then find m ∠ WXZ. 5. (L12) If 𝑋𝑋𝑋𝑋 (Hint: Use the definition of a segment or angle bisector to solve this problem.) A. 62 B. 78 C. 54 D. 45 E. None of the above 6. (L12) If l bisects 𝐷𝐷𝐷𝐷 at point R, DR = 2y + 9, and RE = 3y – 1, then find DE. (Hint: Use the definition of a segment or angle bisector to solve this problem.) A. 64 B. 76 C. 58 D. 49 E. None of the above 7. (L17) Complementary angles _____ equal. A. are always B. are sometimes C. are never D. cannot be E. None of the above 8. (L18) Pairs of _____ angles are always congruent. A. complementary B. supplementary C. acute D. vertical E. obtuse 9. (L21) The _____ between two points is the length of the line segment joining the points. A. linear pair B. angle C. distance D. midpoint E. bisector 10. (L20) A perpendicular bisector is _____ to a line segment and intersects the line segment at its _____. A. perpendicular; endpoint B. adjacent; midpoint C. supplementary; angle D. perpendicular; midpoint E. exterior; linear pair 11. (L20) All _____ angles are congruent. A. acute B. complementary C. supplementary D. adjacent E. right 12. (L21) Use the inch ruler below to measure the distance (in inches) between point P and line n. 1 A. approximately 1 4 inches 3 B. approximately 1 4 inches 3 C. approximately 4 of an inch D. approximately 2 inches E. approximately 1 inch 13. (L16) Find the measures of the complement and the supplement of angle m ∠ ACE = 71. A. complement: 64 supplement: 125 B. complement: 19 supplement: 109 C. complement: 23 supplement: 93 D. complement: 45 supplement: 45 E. None of the above 14. (L16) Find the measures of the complement and the supplement of angle m ∠ M = x + 45. A. complement: 45 supplement: 135 B. complement: 45 – x supplement: 135 – x C. complement: 90 – x supplement: 180 – x D. complement: x – 45 supplement: x – 135 E. complement: x + 45 supplement: x + 135 15. (L17) Find m ∠ SRU in the diagram. A. 54 B. 45 C. 24 D. 48 E. None of the above 16. (L18) Find m ∠ TRU in the diagram. A. 180 B. 144 C. 132 D. 130 E. None of the above Refer to the diagram below for problems 17-19. From each given statement, select the definition, property, postulate, or theorem that leads to the statement you are asked to prove. 17. (L18) Given: Lines AD and XY intersect at point O Prove: ∠ AOX ≌ ∠ DOY A. Pairs of vertical angles are congruent. B. If two angles are a linear pair, then they are congruent. C. Betweenness of Rays D. Definition of congruent angles E. If two angles are complementary to the same angle, then they are congruent. 18. (L20) Given: 𝐴𝐴𝐴𝐴 ⊥ 𝐶𝐶𝐶𝐶; ∠ AOX and ∠ XOB are adjacent angles Prove: ∠ AOX and ∠ XOB are complementary A. If two angles are complementary to the same angle, then they are congruent. B. Definition of complementary angles C. If the exterior sides of a pair of adjacent angles are perpendicular, then the angles are complementary. D. Perpendicular lines intersect to form four right angles. E. If two angles are a linear pair, then they are supplementary. 19. (L19) Given: 𝐴𝐴𝐴𝐴 ⊥ 𝐶𝐶𝐶𝐶 Prove: ∠ DOB is a right angle A. If the exterior sides of a pair of adjacent angles are perpendicular, then the angles are complementary. B. Transitive Property C. Reflexive Property D. A right angle is an angle with a measure of 90. E. Perpendicular lines intersect to form four right angles. 20. (L17) Given: ∠ M ≌ ∠ R and ∠ R ≌ ∠ Z Prove: ∠ M ≌ ∠ Z A. Transitive Property B. If two angles are supplementary to the same angle, then they are congruent. C. Reflexive Property D. Definition of complementary angles E. Definition of congruent angles. 21. (L15) An angle’s measure is 10 less than 4 times its complement. Find the measure of the angle. A. 45 B. 70 C. 75 D. 90 E. None of the above 22. (L16) Twice the complement of an angle is 50 less than the angle’s supplement. Find the measure of the angle. A. 45 B. 50 C. 60 D. 90 E. None of the above  N 23. Select the correct proof from the options listed. Given: 𝑀𝑀𝑀𝑀 ⊥ 𝑁𝑁𝑁𝑁; ∠ 1 and ∠ 2 are adjacent angles Prove: m ∠ 1 + m ∠ 2 = 90º 1 2 M O A. Statements Reasons 1. 𝑀𝑀𝑀𝑀 ⊥ 𝑁𝑁𝑁𝑁 1. Given 2. ∠ 1 and ∠ 2 are vertical angles. 2. Given 3. ∠ MON is a right angle. 3. Perpendicular lines intersect to form right angles. 4. m ∠ MON = 90º 4. Definition of a right angle 5. m ∠ 1 + m ∠ 2 = ∠ MON 5. Betweenness of Rays 6. m ∠ 1 + m ∠ 2 = 90º 6. Transitive Property or Substitution Property B. Statements Reasons 1. 𝑀𝑀𝑀𝑀 ⊥ 𝑁𝑁𝑁𝑁 1. Given 2. m ∠ 1 + m ∠ 2 = 90º 2. Given 3. ∠ MON is a right angle. 3. Perpendicular lines intersect to form right angles. 4. m ∠ MON = 90º 4. Definition of a right angle 5. m ∠ 1 + m ∠ 2 = ∠ MON 5. Betweenness of Rays 6. m ∠ 1 + m ∠ 2 = 90º 6. Transitive Property or Substitution Property C. Statements Reasons 1. 𝑀𝑀𝑀𝑀 ⊥ 𝑁𝑁𝑁𝑁 1. Given 2. ∠ 1 and ∠ 2 are adjacent angles. 2. Given 3. ∠ MON is a right angle. 3. Perpendicular lines intersect to form right angles. 4. m ∠ MON = 90º 4. Definition of a right angle 5. m ∠ 1 + m ∠ 2 = ∠ MON 5. Betweenness of Rays 6. m ∠ 1 + m ∠ 2 = 90º 6. Transitive Property or Substitution Property D. Statements Reasons 1. 𝑀𝑀𝑀𝑀 ⊥ 𝑁𝑁𝑁𝑁 1. Given 2. ∠ 1 and ∠ 2 are adjacent angles. 2. Given 3. ∠ MON is a right angle. 3. Perpendicular lines intersect to form right angles. 4. m ∠ MON = 90º 4. Transitive Property 5. m ∠ 1 + m ∠ 2 = ∠ MON 5. Distributive Property 6. m ∠ 1 + m ∠ 2 = 90º 6. Substitution Property E. Statements Reasons 1. 𝑀𝑀𝑀𝑀 ⊥ 𝑁𝑁𝑁𝑁 1. Given 2. ∠ MON is a right angle. 2. Given 3. ∠ 1 and ∠ 2 are adjacent angles. 3. Perpendicular lines intersect to form right angles. 4. m ∠ MON = 90º 4. Definition of a right angle 5. m ∠ 1 + m ∠ 2 = ∠ MON 5. Betweenness of Rays 6. m ∠ 1 + m ∠ 2 = 90º 6. Transitive Property or Substitution Property 24. Select the correct proof from the options listed. Given: m ∠ 1 = m ∠ 2 1 2 Prove: m ∠ 3 = m ∠ 4 3 4 A. Statements Reasons 1. m ∠ 1 = m ∠ 2 1. Given 2. m ∠ 1 = m ∠ 3 2. Vertical angles are equal. 3. m ∠ 2 = m ∠ 4 3. Vertical angles are equal. 4. m ∠ 3 = m ∠ 2 4. Transitive Property 5. m ∠ 3 = m ∠4 5. Substitution Property B. Statements Reasons 1. m ∠ 1 = m ∠ 2 1. Given 2. m ∠ 1 = m ∠ 3 2. Given 3. m ∠ 2 = m ∠ 4 3. Acute angles are equal. 4. m ∠ 3 = m ∠ 2 4. Transitive Property 5. m ∠ 3 = m ∠ 4 5. Self-evident C. Statements Reasons 1. m ∠ 1 = m ∠ 2 1. Given 2. m ∠ 1 = m ∠ 3 2. Adjacent angles are equal. 3. m ∠ 2 = m ∠4 3. Adjacent angles are equal. 4. m ∠ 3 = m ∠ 2 4. Transitive Property 5. m ∠ 3 = m ∠ 4 5. Substitution Property D. Statements Reasons 1. m ∠ 1 = m ∠ 2 1. Given 2. m ∠ 1 = m ∠ 3 2. Transitive Property 3. m ∠ 2 = m ∠ 4 3. Vertical angles are equal. 4. m ∠ 3 = m ∠ 2 4. Vertical angles are equal. 5. m ∠ 3 = m ∠ 4 5. Substitution Property E. Statements Reasons 1. m ∠ 1 = m ∠ 2 1. Vertical angles are equal. 2. m ∠ 1 = m ∠ 3 2. Given 3. m ∠ 2 = m ∠ 4 3. Complementary angles are equal. 4. m ∠ 3 = m ∠ 2 4. Transitive Property 5. m ∠ 3 = m ∠ 4 5. Substitution Property End of Test