Recall the Angle-Bisector Theorem: If a ray bisects one angle of a triangle, then it divides the opposite side into segments whose lengths are equal. The following question is based on a theorem (not stated) that is the converse of the Angle-Bisector Theorem. Given: NP = MN PQ = MQ = 412 ∠P = 620° ∠M = 360° ∠MZONM in degrees (Hint: MQ) Find: Show that MN/MQ = NP/PQ Prove this by finding the product of the means and the product of the extremes. This implies that NQ bisects MN. Find the measures of the following angles in degrees: ∠MZPNM ∠MZONM
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We are given that NP is parallel to MN, which is parallel to PQ. This means that triangle NMQ is similar to triangle MPQ (by AA similarity). Show more…
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