Question

∠g and ∠h are complementary and ∠g and ∠i are complementary. complete the proof that ∠h ≅ ∠i.

1 ∠g and ∠h are complementary given
2 ∠g and ∠i are complementary given
3 m∠g + m∠h = 90° definition of complementary angles
4 m∠g + m∠i = 90° definition of complementary angles
5 m∠g + m∠h = m∠g + m∠i transitive property of equality
6 m∠h = m∠i properties of addition, subtraction, multiplication, and division
7

Explanation:

Step1: Recall the definition of congruent angles

Congruent angles have equal measures.

Step2: Use the result from step 6

Since \(m\angle H = m\angle I\) (from step 6), by the definition of congruent angles, \(\angle H\cong\angle I\).

Answer:

\(\angle H\cong\angle I\) (by the definition of congruent angles, since \(m\angle H = m\angle I\))