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Step-by-step explanation:
You are given a side and its opposite angle as being congruent to their counterparts in the other triangle. To prove triangle congruence, you need at least 2 sides and an angle, or at least 2 angles and a side, or 3 sides. That is, available congruence postulates are ...
SSS SAS ASA AAS
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Here, we observe that congruence of another angle can be claimed by considering the vertical angles at M. So, our proof can be written as ...
1. ∠LOM≅∠NPM, LM≅NM . . . . given
2. ∠LMO≅∠NMP . . . . vertical angles are congruent
3. ΔLOM≅ΔNPM . . . . AAS congruence postulate