Question

Identify the correct justification for each step, given that ∠1 and ∠2 are complementary, and ∠2 and ∠3 are complementary.
1. ∠1 and ∠2 are complementary
∠2 and ∠3 are complementary
2. m∠1 + m∠2 = 90°
3. m∠2 + m∠3 = 90°
4. m∠1 + m∠2 = m∠2 + m∠3
5. m∠1 = m∠3

Answer 1

Explanation:

1. Given
2. Definition of complementary
3. Definition of complementary
4. Transitive property of equality
5. Addition (subtraction) property of equality

In step 4, we make use of the property that things equal to the same thing are equal to each other.

In step 5, we make use of the fact that subtracting the same quantity (m∠2) from both sides of the equal sign doesn't change the values of any of the other parts of the equation.