Climbers want to determine a halfway point up a vertical cliff.​ If the top and bottom are​ parallel, why is point​ P, where the ropes​ intersect, halfway up the​ cliff?
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Part 1
It is given that
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LM overbar congruent ON overbar .
LP overbar congruent PN overbar .
PO overbar congruent PM overbar .

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because they are vertical angles.
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because they are alternate interior angles.​ Therefore, triangle symbolLMP is congruent to triangle symbolNOP by
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The heights of congruent triangles are​ congruent, so P is halfway up the cliff.