In the given figure- AB - AC and BD - EC then prove that - ADE is an isosceles triangle-

In Δ ABD and Δ AEC AB = AC #160; (given) #8230;(i) ∠ ABC = ∠ ACB #160; #8230;(ii) (angle opposite to equal sides are equal)Also ...

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Standard X

Mathematics

SAS Similarity

In the given ...

Question

In the given figure, $A B = A C$ and $B D = E C$ then prove that $Δ A D E$ is an isosceles triangle.

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Solution

In $Δ A B D$ and $Δ A E C$
$A B = A C$ (given) …(i)
$∠ A B C = ∠ A C B$ …(ii) (angle opposite to equal sides are equal)
Also $B D = E C$ (given) …(iii)
From (i), (ii) and (iii), we have
$Δ A B D = Δ A E C$ (by SAS congruency property)
$A D = A E$ (by c.p.c.t)
Hence, $Δ A D E$ is an isosceles triangle.
Hence proved.

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In the given figure, AB=AC and BD=EC then prove that ΔADE is an isosceles triangle.

In ΔABD and ΔAECAB=AC (given) …(i)∠ABC=∠ACB …(ii) (angle opposite to equal sides are equal)Also BD=EC (given) …(iii)From (i), (ii) and (iii), we haveΔABD=ΔAEC (by SAS congruency property)AD=AE (by c.p.c.t)Hence, ΔADE is an isosceles triangle.Hence proved.

In the given figure, $A B = A C$ and $B D = E C$ then prove that $Δ A D E$ is an isosceles triangle.