Mathematics
In the adjoining figure AC = AE, AB = AD and ∠BAD = ∠CAE. Show that BC = DE.
Triangles
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Answer
Join DE.
Given,
⇒ ∠BAD = ∠CAE
∴ ∠BAD + ∠DAC = ∠CAE + ∠DAC
⇒ ∠BAC = ∠DAE.
In △ABC and △ADE,
AC = AE (Given)
AB = AD (Given)
∠BAC = ∠DAE (Proved)
∴ △ABC ≅ △ADE by SAS axiom.
We know that corresponding sides of congruent triangles are equal.
∴ BC = DE.
Hence, proved that BC = DE.
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