Question

6 given: n is the midpoint of ( overline{lq} ), ( angle nlm cong angle nqp ) prove: ( \triangle mnl cong \triangle pnq ) statements reasons 1. n is the midpoint of ( overline{lq} ) 1. 2. 2. definition of midpoint 3. ( angle lnm cong angle qnp ) 3. 4. ( angle nlm cong angle nqp ) 4. 5. ( \triangle mnl cong \triangle pnq ) 5.

Explanation:

Step1: State given midpoint

Given: $N$ is the midpoint of $\overline{LQ}$

Step2: Derive congruent segments

$\overline{LN} \cong \overline{QN}$

Step3: Identify vertical angles

Vertical Angles Theorem

Step4: State given angle congruence

Given: $\angle NLM \cong \angle NQP$

Step5: Apply ASA congruence

Angle-Side-Angle (ASA) Congruence Postulate

Answer:

1. Given
2. $\boldsymbol{\overline{LN} \cong \overline{QN}}$
3. Vertical Angles Theorem
4. Given
5. Angle-Side-Angle (ASA) Congruence Postulate