Mathematics
In the following figure, AB = EF, BC = DE and ∠B = ∠E = 90°. Prove that AD = FC.
Triangles
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Answer
Given,
⇒ BC = DE
Adding CD on both sides, we get :
⇒ BC + CD = DE + CD
⇒ BD = CE.
In △ ABD and △ FEC,
⇒ ∠ABD = ∠FEC (Both equal to 90°)
⇒ AB = EF (Given)
⇒ BD = CE (Proved above)
∴ ∆ ABD ≅ ∆ FEC (By S.A.S. axiom)
We know that,
Corresponding parts of congruent triangles are equal.
∴ AD = FC.
Hence, proved that AD = FC.
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