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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