Math  /  Geometry

QuestionGiven: LPON\overline{L P} \| \overline{O N} and LO\overline{L O} bisects PN\overline{P N} at point MM Prove: MLPMON\triangle M L P \cong \triangle M O N

Studdy Solution
Aplicar el criterio de congruencia de triángulos:
1. LPMONM\angle LPM \cong \angle ONM (ángulos correspondientes).
2. LMPMON\angle LMP \cong \angle MON (ángulos alternos internos).
3. PMMN\overline{PM} \cong \overline{MN} (dado que MM es el punto medio de PN\overline{PN}).

Por el criterio de congruencia ALA (Ángulo-Lado-Ángulo), MLPMON\triangle MLP \cong \triangle MON.

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