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Mathematics, 22.11.2019 02:31 iamsecond235p318rq
The two-column proof below describes the statements and reasons for proving that corresponding angles are congruent:
what is the missing statement for step 5?
a. m∠sqv + m∠vqt = 180°
b. m∠sqv = m∠sqt
c. m∠sqv + m∠sqt = m∠vqt
d. m∠sqv + m∠sqt = 180°
step statements reasons
1 segment uv is parallel to segment wz given
2 points s, q, r, and t all lie on the same line. given
3 m∠sqt = 180° definition of a straight angle
4 m∠sqv + m∠vqt = m∠sqt angle addition postulate
5 substitution property of equality
6 m∠vqt + m∠zrs = 180° same-side interior angles theorem
7 m∠sqv + m∠vqt = m∠vqt + m∠zrs substitution property of equality
8 m∠sqv + m∠vqt − m∠vqt = m∠vqt + m∠zrs − m∠vqt
m∠sqv = m∠zrs subtraction property of equality
∠sqv ≅ ∠zrs definition of congruency
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