Question

Sylvie has started a proof of the Triangle Angle Sum Theorem. Which answer choice correctly completes her proof?

Sylvie's Proof: Given the diagram shown, ∠1≅∠5
∠
1
≅
∠
5
; ∠2≅∠4
∠
2
≅
∠
4
because alternate interior angles are congruent when lines are parallel. Then, I know that m∠1=m∠5
𝑚
∠
1
=
𝑚
∠
5

Answer 1

To complete Sylvie's proof of the Triangle Angle Sum Theorem, you can add the following statement:

"Since ∠1 and ∠2 are supplementary angles to ∠3, we can write the equation m∠1 + m∠2 + m∠3 = 180°. Because we have already established that ∠1 ≅ ∠5 and ∠2 ≅ ∠4, we can substitute to find m∠5 + m∠4 + m∠3 = 180°. Therefore, the sum of the measures of the angles in any triangle is 180°."

So, the final statement in Sylvie's proof can be:

"Thus, m∠5 + m∠4 + m∠3 = 180°, which proves the Triangle Angle Sum Theorem."