Question

complete the paragraph proof given: <1 and <2 are supplementary and <2 and <3 are supplementary Prove: <1 is congruent to <3

Answer 1

Given: ∠1 and ∠2 are supplementary (meaning ∠1 + ∠2 = 180 degrees) and ∠2 and ∠3 are supplementary (meaning ∠2 + ∠3 = 180 degrees).

To Prove: ∠1 is congruent to ∠3.

Proof:

Since ∠1 and ∠2 are supplementary, we can write the equation ∠1 + ∠2 = 180 degrees. (1)

Similarly, since ∠2 and ∠3 are supplementary, we can write the equation ∠2 + ∠3 = 180 degrees. (2)

We want to prove ∠1 is congruent to ∠3, which means that ∠1 and ∠3 have the same measure.

We can rewrite equation (1) as ∠2 = 180 - ∠1. (3)

Plugging equation (3) into equation (2), we have (180 - ∠1) + ∠3 = 180.

Simplifying, we get 180 - ∠1 + ∠3 = 180.

Rearranging, we have ∠3 - ∠1 = 0.

Adding ∠1 to both sides, we have ∠3 = ∠1.

Therefore, we have proven that ∠1 is congruent to ∠3.