Unit 2 – Similarity, Congruence, and Proofs

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

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°

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

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°

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°

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°

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°

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°

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°

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.

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

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°

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

Find m∠2 if m∠1= 5x +12 and m∠3= 4x −12 . Question 13 Find m∠2 if m∠1= 5x +12 and m∠3= 4x −12 . 68°

Find m∠3 if m∠1= 3x +1 and m∠2= 2(x +7). Question 14 Find m∠3 if m∠1= 3x +1 and m∠2= 2(x +7). 40°

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.