Question

3 given: ∠1 and ∠2 form a right angle; m∠1 + m∠3 = 90° prove: ∠2 ≅ ∠3 statements reasons 1. ∠1 and ∠2 form a right angle 1. given 2. ∠1 and ∠2 are complementary 2. 3. m∠1 + m∠3 = 90° 3. 4. ∠1 and ∠3 are complementary 4. 5. ∠2 ≅ ∠3 5.

Explanation:

Step1: Define complementary angles

If two angles form a right - angle, they are complementary. Since $\angle1$ and $\angle2$ form a right - angle, $\angle1$ and $\angle2$ are complementary.

Step2: Given information

We are given that $m\angle1 + m\angle3=90^{\circ}$.

Step3: Define complementary angles again

If the sum of the measures of two angles is $90^{\circ}$, the two angles are complementary. So, $\angle1$ and $\angle3$ are complementary.

Step4: Use the congruence of complementary angles

If $\angle1$ and $\angle2$ are complementary and $\angle1$ and $\angle3$ are complementary, then $\angle2\cong\angle3$ (if two angles are complementary to the same angle, then they are congruent).

Answer:

1. Definition of complementary angles
2. Given
3. Definition of complementary angles
4. Congruence of complementary angles