Question

Given: 1 and 2 are supplements, and 3 and 2 are supplements.

Prove: 1 3
Complete the missing parts of the paragraph proof.
By the definition of --- angles, the sum of the measures of angles 1 and 2 is 180 degrees. Likewise, the sum of the measures of angles --- is 180 degrees. By the ---property, m1 + m2 = m3 + m2. Subtract the measure of angle --- from each side. You get m1 = m3, or 1 3, by the definition of congruence.

Answer 1

By the definition of supplementary angles, the sum of the measures of angles 1 and 2 is 180 degrees. Likewise, the sum of the measures of angles 3 and 2 is 180 degrees. By the substitution property, m1 + m2 = m3 + m2. Subtract the measure of angle 2 from each side. You get m1 = m3, or 1 3, by the definition of congruence.

Answer 2

The correct answers are:

Supplementary; ∠2 and ∠3; substitution; 2.

Step-by-step explanation:

Supplementary angles are angles whose measures sum to 180°. Thus this is the first answer.

Since we are told that ∠2 and ∠3 are supplementary, their measures sum to 180° and they are the second answer.

We know that m∠1 + m∠2 = 180° and m∠2 + m∠3 = 180°. We can substitute "m∠2 + m∠3" for 180° in the first equation; this is the substitution property.

To isolate m∠1 on the right, we will subtract m∠2 from each side, and get that m∠1 = m∠3 and the angles are congruent.