Identify the proof to show that △LMQ≅△NPQ, where Q is the midpoint of LN¯¯¯¯¯ and MP¯¯¯¯¯¯, ∠L≅∠N, and LM¯¯¯¯¯¯≅NP¯¯¯¯¯.

The figure shows two triangles L M Q and N P Q. The triangles have a common vertex Q. Points M, Q, P lie on one line. Points N, Q, L lie on one line.

1. ∠L≅∠N (given)2. Q is midpoint of LN¯¯¯¯¯ and MP¯¯¯¯¯¯ (given)3. LQ¯¯¯¯¯≅QN¯¯¯¯¯¯; MQ¯¯¯¯¯¯≅QP¯¯¯¯¯ (definition of midpoint)4. LM¯¯¯¯¯¯≅QP¯¯¯¯¯ (given)5. ∠LQM≅∠NQP (vertical angles theorem)6. ∠M=∠P (third angles theorem)7. △LMQ≅△NPQ (definition of congruent triangles)

1. ∠L≅∠N (given)2. Q is midpoint of LN¯¯¯¯¯ and MP¯¯¯¯¯¯ (given)3. LQ¯¯¯¯¯≅QN¯¯¯¯¯¯; MQ¯¯¯¯¯¯≅QP¯¯¯¯¯ (definition of midpoint)4. LM¯¯¯¯¯¯≅NP¯¯¯¯¯¯ (given)5. ∠LQM≅∠NQP (third angles theorem)6. ∠M=∠P (vertical angles theorem)7. △LMQ≅△NPQ (definition of congruent triangles)

1. ∠L≅∠N (given)2. Q is midpoint of LN¯¯¯¯¯ and MP¯¯¯¯¯¯ (given)3. LQ¯¯¯¯¯≅QN¯¯¯¯¯¯; MQ¯¯¯¯¯¯≅QP¯¯¯¯¯ (definition of midpoint)4. LM¯¯¯¯¯¯≅NP¯¯¯¯¯¯ (given)5. ∠LQM≅∠NQP (vertical angles theorem)6. ∠M=∠P (third angles theorem)7. △LMQ≅△NPQ (definition of congruent triangles)

1. ∠L≅∠N (given)2. Q is midpoint of LN¯¯¯¯¯ and MP¯¯¯¯¯¯ (given)3. LQ¯¯¯¯¯≅QN¯¯¯¯¯¯; MQ¯¯¯¯¯¯≅QP¯¯¯¯¯ (definition of midpoint)4. LM¯¯¯¯¯¯≅NP¯¯¯¯¯¯ (given)5. ∠LQM≅∠NQP (vertical angles theorem)6. ∠M=∠N (third angles theorem)7. △LMQ≅△NPQ (definition of congruent triangles)