Mathematics
In the following figure, AB = AD, AC = AE and ∠BAD = ∠CAE.
Prove that : BC = ED.
Triangles
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Answer
Given: AB = AD, AC = AE and ∠BAD = ∠CAE.
⇒ ∠BAD + ∠DAC = ∠CAE + ∠DAC (Adding ∠DAC on both sides)
⇒ ∠BAC = ∠DAE
In Δ BAC and Δ DAE,
AB = AD (Given)
∠BAC = ∠DAE (Proved above)
AC = AE (Given)
Using SAS congruence criterion,
Δ BAC ≅ Δ DAE
By corresponding parts of congruent triangles,
BC = DE
Hence, BC = DE.
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