Question

1. given: ( overline{lm} cong overline{no} ), and ( angle m cong angle o ) prove ( \triangle mpl cong \triangle opn ) 6. ( overline{pr} cong overline{sq} ) 6. cpctc

Explanation:

Step 1: Fill in the second statement

Since we are given that \( \angle M\cong\angle O\), so statement 2 is \( \angle M\cong\angle O\) and justification is "Given"

Step 2: Justify \( \angle LPM\cong\angle NPO\)

Vertical angles are congruent. So justification for \( \angle LPM\cong\angle NPO\) is "Vertical angles are congruent"

Step 3: Justify \( \triangle MPL\cong\triangle OPN\)

We have two angles and a non - included side congruent. By the AAS (Angle - Angle - Side) congruence criterion, \( \triangle MPL\cong\triangle OPN\). So justification for \( \triangle MPL\cong\triangle OPN\) is "AAS (Angle - Angle - Side) Congruence Theorem"

Answer:

Statements	Justifications
2. \( \angle M\cong\angle O\)	2. Given
3. \( \angle LPM\cong\angle NPO\)	3. Vertical angles are congruent
4. \( \triangle MPL\cong\triangle OPN\)	4. AAS (Angle - Angle - Side) Congruence Theorem