Final answer:
By subtracting the measure of angle B from both sides of the given equation, it can be proven effectively that the measure of angle C is equal to the measure of angle A, using the Subtraction Property of Equality.
Step-by-step explanation:
To prove that m∠C = m∠A given that m∠A + m∠B = m∠B + m∠C, we can follow a paragraph proof approach.
First, let us look at the given equation and rearrange it by subtracting m∠B from both sides, getting m∠A = m∠C. This is a straightforward application of the Subtraction Property of Equality. It shows that when we remove the common angle measurement from both sides of the equation, the measurements of angles A and C are equal.
Hence, we have proved that the measure of angle C is equal to the measure of angle 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.