Mathematics
In figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Show that BC = DE.
Triangles
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Answer
Given :
AC = AE, AB = AD,
⇒ ∠BAD = ∠EAC.
Adding ∠DAC to both sides of this equation, we get :
⇒ ∠BAD + ∠DAC = ∠EAC + ∠DAC
⇒ ∠BAC = ∠DAE.
In Δ BAC and Δ DAE,
⇒ AB = AD (Given)
⇒ ∠BAC = ∠DAE (Proved above)
⇒ AC = AE (Given)
∴ Δ BAC ≅ Δ DAE (By S.A.S. congruence rule)
We know that,
Corresponding parts of congruent triangles are equal.
∴ BC = DE (By C.P.C.T.)
Hence, proved that BC = DE.
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