Question

Sample Response: We are given that the sum of the measures of angles A and B is equal to the sum of the measures of angles B and C. The measure of angle B is equal to itself by the reflexive property, so you can subtract that measure from both sides of the equation. Now the measure of angle A equals the measure of angle C. By the symmetric property, this means the measure of angle C equals the measure of angle A.What did you include in your response? Check all that apply.

Answer 1

The sum of angles A and B equals the sum of angles B and C, which after subtracting angle B, indicates that angle A equals angle C, making them congruent.

Step-by-step explanation:

We are given that the sum of the measures of angles A and B is equal to the sum of the measures of angles B and C. Since the measure of angle B is equal to itself, we can apply the reflexive property and subtract it from both sides of the equation. This leaves us with the measure of angle A being equal to the measure of angle C. By the symmetric property, it also means that the measure of angle C is equal to the measure of angle A, concluding that angles A and C are congruent.

Answer 2

A paragraph to prove the statement m∠C = m∠A is;

• We are given that the sum of the measures of angles A and B is equal to the sum of the measures of angles B and C. The measure of angle B is equal to itself by the reflexive property, so you can subtract that measure from both sides of the equation. Now the measure of angle A equals the measure of angle C. By the symmetric property, this means the measure of angle C equals the measure of angle A.

Which paragraph proves the statement?

Given: m∠A + m∠B = m∠B + m∠C

Prove: m∠C = m∠A

Sum of m∠A + m∠B = m∠B + m∠C

m∠B = m∠B (reflective property)

So,

m∠A = m∠C

By symmetric property

Hence, m∠C = m∠A

Complete question:

Given: m∠A + m∠B = m∠B + m∠C

Prove: m∠C = m∠A

Write a paragraph proof to prove the statement.