Question

try it! write a paragraph proof

1. write a paragraph proof of the congruent complements theorem.

given: ∠1 and ∠2 are complementary. ∠2 and ∠3 are complementary.
prove: ∠1≅∠3

Explanation:

Step1: Define complementary angles

Complementary angles add up to 90 degrees. So, $\angle1+\angle2 = 90^{\circ}$ and $\angle2+\angle3=90^{\circ}$ since $\angle1$ and $\angle2$ are complementary and $\angle2$ and $\angle3$ are complementary.

Step2: Rearrange equations

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

Step3: Apply transitive property

Since $\angle1=90^{\circ}-\angle2$ and $\angle3=90^{\circ}-\angle2$, by the transitive property of equality, $\angle1=\angle3$. And if two angles have the same measure, they are congruent. So, $\angle1\cong\angle3$.

Answer:

The proof shows that if $\angle1$ and $\angle2$ are complementary and $\angle2$ and $\angle3$ are complementary, then $\angle1\cong\angle3$ by using the definition of complementary angles, equation - rearrangement, and the transitive property of equality.