Question

Given: p || q, and r || s. Prove: ∠4 is supplementary to ∠15. What is the missing step in the given proof?

a. Statement: m∠4 = m∠15, Reason: Substitution property of equality
b. Statement: m∠4 + m∠8 = 180°, Reason: Definition of supplementary angles
c. Statement: ∠7 and ∠8 are supplementary, Reason: Linear pair theorem
d. Statement: m∠4 = m∠16, Reason: Transitive property of equality
e. Statement: ∠15 and ∠8 are supplementary, Reason: Transitive property of equality

Answer 1

The missing step in the given proof is that ∠4 and ∠16 are congruent, which can be proven using the transitive property of equality.

Step-by-step explanation:

The missing step in the given proof is option d. Statement: m∠4 = m∠16, Reason: Transitive property of equality.

To prove that ∠4 is supplementary to ∠15, we need to show that the measures of ∠4 and ∠15 add up to 180°. Given that p || q and r || s, we know that ∠4 and ∠16 are corresponding angles, and ∠16 is congruent to ∠15. Therefore, by the transitive property of equality, we can conclude that ∠4 is also congruent to ∠15 (m∠4 = m∠16). Hence, ∠4 and ∠15 are supplementary angles, and the missing step is to state that m∠4 = m∠16 using the transitive property of equality.