Question

given: q||r
prove: ∠1≅∠3
statements reasons
q||r given
<1 and <3 are alt exterior <s alt exterior <s thrm
<1 and <3 are congruent alt exterior <s thrm

Explanation:

Step1: Use the property of vertical angles

$\angle1$ and $\angle2$ are vertical angles. By the vertical angles theorem, $\angle1\cong\angle2$.

Step2: Use the property of alternate interior angles

Since $q\parallel r$, by the alternate interior angles theorem, $\angle2\cong\angle3$.

Step3: Use the transitive property of congruence

If $\angle1\cong\angle2$ and $\angle2\cong\angle3$, then by the transitive property of congruence (if $a = b$ and $b = c$, then $a = c$ for congruent angles), $\angle1\cong\angle3$.

Answer:

The proof is completed as shown in the steps above, so $\angle1\cong\angle3$.