In an isosceles $Δ A B C, A B = A C, D$ and $E$ are two points on the sides $A B$ and $A C$ respectively such that $A D = A E$ . Prove that $Δ A B E ≅ Δ A C D$ .

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Solution

In $Δ A B E$ & $Δ A C D$
$A B = A C$ (given)
$A E = A D$ (given)
$∠ A = ∠ A$ (common)
$∴$ $Δ A B E ≅ Δ A C D$
( $S A S$ congruency)

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In an isosceles ΔABC, AB=AC, D and E are two points on the sides AB and AC respectively such that AD=AE. Prove that ΔABE≅ΔACD.

In ΔABE & ΔACDAB=AC (given)AE=AD (given)∠A=∠A (common)∴ ΔABE≅ΔACD(SAS congruency)

In an isosceles $Δ A B C, A B = A C, D$ and $E$ are two points on the sides $A B$ and $A C$ respectively such that $A D = A E$ . Prove that $Δ A B E ≅ Δ A C D$ .

In $Δ A B E$ & $Δ A C D$
$A B = A C$ (given)
$A E = A D$ (given)
$∠ A = ∠ A$ (common)
$∴$ $Δ A B E ≅ Δ A C D$
( $S A S$ congruency)