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In triangle ABC, AD is perpendicular …

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In triangle ABC, AD is perpendicular to BC, such that ADsquare = BD.CD. Prove that triangle ABC is right-angled at A.

Posted by Madhavi Sharma 6 years, 11 months ago

CBSE > Class 10 > Mathematics

1 answers

Himanshi Sharma 6 years, 11 months ago

Proof: In right triangle ADB and ADC so, by Pythagoras theorem, AB^2=AD^2+BD^2.................(1) AC^2=AD^2+DC^2..................(2) AB^2+AC^2=2AD^2+BD^2+DC^2 =2BD.CD+BD^2+CD^2 [given:AB^2=BD.CD] (BD+CD)^2=BC^2 Thus in triangle ABC we have, AB^2+AC^2=BC^2 Hence, triangle ABC is a right triangle right angled at A. Angle BAC = 90°

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