In triangle PQR,PQ=PR and S is any point on QR prove that PQ2-PS2=QS RS - Maths - Triangles

Question

In triangle PQR,PQ=PR and S is any point on QR prove that
PQ2 -PS2=QS RS

Lovina Kansal · Accepted Answer

Dear student
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Draw PT⊥QRIn △PTQ and △PTR, we havePQ=PRPT=PT   [common]∠Q=∠R    [∵PQ=PR]∴△PTQ≅△PTR⇒QT=RTSince △PTS and △PQT are right triangles right-angled at T
Therefore, PS2=PT2+ST2 and PQ2=PT2+QT2PQ2-PS2=QT2-ST2⇒PQ2-PS2=QT-STQT+ST⇒PQ2-PS2=QT-STRT+ST     [∵QT=RT]⇒PQ2-PS2=QS
SR
Regards

In triangle PQR,PQ=PR and S is any point on QR.prove that PQ2 -PS2=QS.RS

In triangle PQR,PQ=PR and S is any point on QR.prove that PQ² -PS²=QS.RS