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7th
Maths
Congruence of Triangles
Criteria for Triangle Congruence
In the given figure, AD is ...
MATHS
In the given figure, AD is perpendicular to BC and EF∥BC, 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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ANSWER
AD is perpendicular to EF
⇒∠EAD=∠FAD=90
∘
∠EAB=∠FAC (given)
⇒∠EAD−∠EAB=∠FAD−∠FAC
⇒∠BAD=∠CAD
In △ABD and △ACD
∠BAD=∠CAD [proved above]
∠ADB=∠ADC=90
∘
[Given AD is perpendicular on BC]
and AD=AD
△ABD≅△ACD [By ASA]
Hence proved.
∠ABD=∠ACD⇒AB=AC and BD=CD [By C.P.C.T]
⇒2x+3=3y+1 and x=y+1
⇒2x−3y=−2 and x−y=1
Substituting 2(1+y)−3y=−2 Substituting y=4 in x=1+y
x=1+y 2+2y−3y=−2 x=1+4
−y=−2−2 x=5
−y=−4