Question

Write the name or statement of the definition, postulate, or theorem that justifies the statement about the diagram.

If ∠4 is complementary to ∠5 and ∠6 is complementary to ∠5 then $\angle 4\cong \angle 6$.

Short answer

The name of the theorem which justifies the statement about the given diagram is Theorem of Congruence of Angles and Complementary Angles.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Write the theorem of congruence of angles and complementary angles.

The theorem of congruence of angles and complementary angles states thatif two angles are complements of the same angle then the two angles are congruent.

Step 3. Write the name of the theorem that justifies the statement about the given diagram.

Given that∠4 is complementary to∠5 and∠6 is complementary to∠5.

That implies the angles∠4 and∠6 are complements of the same angle∠5.

Therefore, by using the theorem of congruence of angle and complementary angles it can be said that the angles∠4 and∠6 are congruent angles.

That implies, $\angle 4\cong \angle 6$.

Therefore, the name of the theorem that justifies the statement about the given diagram is theorem of congruence of angles and complementary angles.