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Question

In the given figure, AD is perpendicular to BC and EFBC, if EAB=FAC, show that triangles ABD and ACD are congruent.
Also, find the values of x and y if AB=2x+3,AC=3y+1,BD=x and DC=y+1
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Solution

AD is perpendicular to EF
EAD=FAD=90
EAB=FAC (given)
EADEAB=FADFAC
BAD=CAD
In ABD and ACD
BAD=CAD [proved above]
ADB=ADC=90 [Given AD is perpendicular on BC]
and AD=AD
ABDACD [By ASA]
Hence proved.
ABD=ACDAB=AC and BD=CD [By C.P.C.T]
2x+3=3y+1 and x=y+1
2x3y=2 and xy=1
Substituting 2(1+y)3y=2 Substituting y=4 in x=1+y
x=1+y 2+2y3y=2 x=1+4
y=22 x=5
y=4

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