Question

proof:
statements reasons

1. \\( \angle 1 \cong \angle 2 ; m \perp p \\) 1.
2. 2. def. of linear pair
3. 3. if \\( 2 \cong \angle s \\) form a linear pair, they are right \\( \angle s \\).
4. \\( \angle 3 \\) is a right angle. 4.
5. 5. all right \\( \angle s \\) are congruent.

\\( \angle 1 \\) and \\( \angle 2 \\) are rt. \\( \angle s \\). \\( \perp \\) lines form 4 rt. \\( \angle s \\). given \\( \angle 2 \cong \angle 3 \\)
\\( \angle 1 \\) and \\( \angle 2 \\) form a linear pair.

Explanation:

Step1: Fill in Reason 1

The first statement is given, so the reason is "Given".

Step2: Fill in Statement 2

Since the reason is "Def. of linear pair", the statement should be "$\angle1$ and $\angle2$ form a linear pair".

Step3: Fill in Statement 3

Based on the reason "If 2 ≅ ∠s form a linear pair, they are right ∠s" and the previous statements, the statement is "$\angle1$ and $\angle2$ are rt. ∠s".

Step4: Fill in Reason 4

Since $m\perp p$ (given in statement 1) and the property that perpendicular lines form right angles, the reason is "$\perp$ lines form 4 rt. ∠s".

Step5: Fill in Statement 5

Since the reason is "All right ∠s are congruent" and we know $\angle2$ and $\angle3$ are right angles (from previous steps), the statement is "$\angle2\cong\angle3$".

Answer:

1. Given
2. $\angle1$ and $\angle2$ form a linear pair
3. $\angle1$ and $\angle2$ are rt. ∠s
4. $\perp$ lines form 4 rt. ∠s
5. $\angle2\cong\angle3$