Final answer:
The statement mZC equals mZA is proven by applying the Commutative Property of Addition to the given equation and then simplifying it by subtracting mZB from both sides.
Step-by-step explanation:
To prove that mZC equals mZA, start with the given equation mZA + mZB = mZB + mZC.
This equation follows the Commutative Property of Addition, which states that numbers can be added in any order without changing the sum.
We are given that mZA + mZB = mZB + mZC. We want to prove that mZC = mZA. To prove this, we can use the commutative property of addition, which states that A + B = B + A.
Therefore, we can rearrange the given equation as mZB + mZA = mZB + mZC. Now, we can apply the subtraction property of equality, which states that if a = b, then a - c = b - c.
By subtracting mZB from both sides of the equation, we get mZA = mZC.
An example of this property is that 2 + 3 is equal to 3 + 2. Applying this property, we simplify the given equation by subtracting mZB from both sides, leaving us with mZA = mZC.
This final equation shows that the measure of angle ZA is equal to the measure of angle ZC, thus proving the initial statement.