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CBSE Class 10 Answered

In triangle abc apad perpendicular to BC such that ADsq equal to bd into cd. Prov that triangle ABC is right angled at A
Asked by sumitkain2016 | 27 Feb, 2019, 02:51: PM
answered-by-expert Expert Answer
Given condition : AD2 = BD × CD   or   begin mathsize 12px style fraction numerator A D over denominator B D end fraction equals fraction numerator C D over denominator A D end fraction end style  .......................(1)
from eqn.(1) , we observe, sides of right angles of ΔABD are in same ratio to the sides of right angle of ΔADC
 
Hence ΔABD and ΔADC are similar triangles.
 
In similar triangles angles oppposit to equivalent side are equal.
 
Hence begin mathsize 12px style angle end styleBAD = begin mathsize 12px style angle end styleACD  and begin mathsize 12px style angle end styleABD = begin mathsize 12px style angle end styleDAC
we have begin mathsize 12px style angle end styleABD + begin mathsize 12px style angle end styleBAD = 90º.  Hence begin mathsize 12px style angle end styleDAC+begin mathsize 12px style angle end styleBAD = begin mathsize 12px style angle end styleBAC = 90°
Answered by Thiyagarajan K | 27 Feb, 2019, 06:36: PM

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