Question

Given: m∠A + m∠B = m∠B + m∠C Prove: m∠C = m∠A Write a paragraph proof to prove the statement.

Answer 1

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.

Answer 2

The correct answer is:

Given: m∠A + m∠B = m∠B + m∠C

Prove: m∠A = m∠C

Starting with our given statement, m∠A + m∠B = m∠B + m∠C, we can use the subtraction property of equality to subtract m∠B from each side:

m∠A + m∠B - m∠B = m∠B + m∠C - m∠B

When we subtract something from itself, it equals 0. This leaves us with:

m∠A + 0 = m∠C + 0

Adding 0 to anything leaves it as it was. This gives us:

m∠A= m∠C