Question

1. ∠2≅∠3
2. m∠2 = m∠3
3. ∠1 and ∠2 form a linear - pair
4. ∠1 and ∠2 are supplementary
5. m∠1 + m∠2 = 180°
6. m∠1 + m∠3 = 180°
7. ∠1 and ∠3 are supplementary
8. given
9. def of congruence
10. given
11. def of supplementary

5.
6.

1. def of supplementary

Explanation:

Step1: Identify given information

Given $\angle2\cong\angle3$ (from statement 1) and $\angle1$ and $\angle2$ form a linear - pair (from statement 3).

Step2: Use linear - pair property

Since $\angle1$ and $\angle2$ form a linear - pair, by the definition of a linear - pair, $m\angle1 + m\angle2=180^{\circ}$ (statement 5).

Step3: Use congruent - angle substitution

Because $\angle2\cong\angle3$, then $m\angle2 = m\angle3$ (statement 2). Substitute $m\angle2$ with $m\angle3$ in $m\angle1 + m\angle2 = 180^{\circ}$, we get $m\angle1 + m\angle3=180^{\circ}$ (statement 6).

Step4: Use supplementary - angle definition

If $m\angle1 + m\angle3 = 180^{\circ}$, then by the definition of supplementary angles, $\angle1$ and $\angle3$ are supplementary (statement 7).

Answer:

The proof is completed as shown above, demonstrating that if $\angle2\cong\angle3$ and $\angle1$ and $\angle2$ form a linear - pair, then $\angle1$ and $\angle3$ are supplementary.