In ∆PQR,PM perpendicular to QR If PM PM=QM MR Prove:: Angle QPR=90 - Maths - Triangles

Question

In ∆PQR,PM perpendicular to QR If PM PM=QM MR Prove:: Angle
QPR=90°

Ashwini Kumar · Accepted Answer

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We have,     PM PM=QM
MR⇒PMRM=QMPMAnd ∠PMQ=∠RMP=90°∴△PMQ~△RMP     By SAS similarityNow ∠QPM=∠PRM=θ  (say)And ∠PRM+∠MPR=90°⇒∠MPR=90°-∠PRM=90°-θNow,∠QPR=∠QPM+∠MPR=θ+90°-θ=90°

In ∆PQR,PM perpendicular to QR. If PM.PM=QM.MR Prove:: Angle QPR=90°