Question

prove the congruent complements theorem. if two angles are complements of the same angle, then the two angles are congruent. given: ∠1 and ∠2 are complementary ∠3 and ∠2 are complementary. choose the correct statement of what is to be proved. prove:

Explanation:

Step1: Define complementary angles

If two angles are complementary, their sum is 90 degrees. So, $\angle1+\angle2 = 90^{\circ}$ and $\angle3+\angle2=90^{\circ}$.

Step2: Express $\angle1$ and $\angle3$

From $\angle1+\angle2 = 90^{\circ}$, we can get $\angle1=90^{\circ}-\angle2$. From $\angle3+\angle2 = 90^{\circ}$, we can get $\angle3=90^{\circ}-\angle2$.

Step3: Prove congruence

Since $\angle1 = 90^{\circ}-\angle2$ and $\angle3=90^{\circ}-\angle2$, then $\angle1=\angle3$.

Answer:

$\angle1\cong\angle3$