Question

Given: mzA + m2B = mzB + m2C

Prove: mzC = mzA
Write a paragraph proof to prove the statement.

A) Subtract m2B from both sides of the equation.
B) Use the properties of angles to manipulate the equation.
C) Apply the transitive property of equality.
D) Conclude that mzC = mzA.

Answer 1

To prove mzC = mzA, we can subtract m2B from both sides of the equation and then manipulate the equation using the properties of angles. Applying the transitive property of equality allows us to simplify the equation and conclude that mzA = mzC.

Step-by-step explanation:

To prove mzC = mzA from the given equation mzA + m2B = mzB + m2C, we can follow these steps:

1. First, subtract m2B from both sides of the equation to isolate mzA: mzA = mzB + m2C - m2B
2. Next, combine like terms on the right side of the equation: mzA = mzB - m2B + m2C
3. Using the properties of angles, we can rewrite mzB - m2B as mzB - m2B + 0°, since subtracting 0° does not change the value.
4. Now, applying the transitive property of equality, we have mzA = mzB + 0° + m2C.
5. Since adding 0° does not change the value, we can simplify to mzA = mzB + m2C.
6. Finally, noticing that mzB + m2C = mzC according to the equation given, we can conclude that mzA = mzC.