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Given BE and CF are the altitudes of the ∆ABC.P,Q are on BE and extension of CF respectively, such that BP=AC,CQ=AB, prove that AP is perpendicular to AQ

Given BE and CF are the altitudes of the ∆ABC.P,Q are on BE and extension of CF respectively, such that BP=AC,CQ=AB, prove that AP is perpendicular to AQ

Grade:12th pass

1 Answers

Prasanjeet Nayak
13 Points
2 years ago

From AB perpendicular to CQ and BE perpendicular to AC

angleABE=angleQCA

SinceAB=CQ and BP =CA,

TriangleABP TriangleQCA (S.A.S.)

 angleBAP angleCQA,

angleQAP angleQAF + angleBAP angleQAF + angleCQA 
= 180 °- 90 = 90

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