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

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

As angles A+B=B+C

SO ... A+B-B = B+C-B. (we subtract B from each side)

so ... A = C

so it is proved that angle A is equal to angle B!