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Geometry Proofs Review Quiz: Lines and Angles Theorems

Test your knowledge of proving theorems about lines and angles with this quiz. Solve questions involving linear pairs, transversals, parallel lines, and supplementary angles.

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Geometry Proofs Review Quiz: Lines and Angles Theorems

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  1. Unit 2 – Similarity, Congruence, and Proofs Review Quiz #8 Proving Theorems about Lines and Angles

  2. Question 1 In the diagram below, ∠1 and ∠2 are a linear pair. Find m∠1 if m∠1= 2x −9 and m∠2=10x +9. 21°

  3. Question 2 Find m∠4 in the diagram below if m∠2= 9(x +6) and m∠4 = 2(5x +21) . 162°

  4. Question 3 In the diagram below, l is the transversal of the parallel lines m and n. Find m∠3 if m∠4 =5(x +11) and m∠5=11x −17 . 65°

  5. Question 4 In the diagram below, l is the transversal of the parallel lines m and n. Find m∠8 if m∠2= 3x + 46 and m∠8= 4x . 24°

  6. Question 5 In the diagram below, l is the transversal of the parallel lines m and n. Find m∠5 if m∠3= 2(3x − 4) and m∠5= 5(3x + 4) . 140°

  7. Question 6 If m∠1= 2x −9 and m∠2=10x −3, find m∠4 given that lines k and l intersect as shown below. 157°

  8. Question 7 If m∠1= 4x and m∠4 =3x −1 in the diagram below, find m∠2 if ∠3 is a right angle. 38°

  9. Question 8 If m∠1= x +7, m∠2= 2(x +2) , and m∠4 = 2(x +13) in the diagram below, find m∠4 . 56°

  10. Question 9 In the proof of the Vertical Angles Theorem below, what are the reasons for the statements listed? Refer to the diagram given. In the diagram, ∠3 and ∠1 form a linear pair and ∠1 and ∠4 form a linear pair. Prove that ∠3∠4 . Given Supplement Theorem Angles supplementary to the same angles or to congruent angles are congruent.

  11. Question 10 Given the diagram and the information below, determine what information is missing from the proof. ∠DBA∠DBC ; Reflexive Property; ∆EBA≅∆EBC

  12. Question 11 There are two sets of parallel lines in the diagram below. Find m∠2 if m∠1=10x − 4 and m∠3= 7x +20 . 76°

  13. Question 12 Find m∠1 if m∠2= 5x and m∠3= 6x −7 . 85°

  14. Question 13 Find m∠2 if m∠1= 5x +12 and m∠3= 4x −12 .

  15. Question 14 Find m∠3 if m∠1= 3x +1 and m∠2= 2(x +7).

  16. Question 15 Given two sets of parallel lines in the diagram below, what is the relationship between ∠6 and ∠15 ? ∠6∠11 since they are alternate exterior angles and alternate exterior angles are congruent. Then, by corresponding angles, ∠11∠15 . Therefore, ∠6∠15 by the Transitive Property.

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