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State whether the following statement is true or false.
In a quadrilateral ACBD, AC = AD and AB bisects $∠ A$ (see figure), then

$Δ A B C ≅ Δ A B D$ and BC = BD.

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True

False

answer is A.

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Detailed Solution

We have been given a quadrilateral ACBD in which, AC=AD and AB line bisects

∠ A .

From the given figure since AB line bisects

∠ A

, then,

Consider ∆ABC and ∆ABD,

A C = A D (Given)

A B = A B (Common)

So, by SAS congruence criteria, we proved that:

We know that corresponding parts of congruent triangles are equal.

∴ B C = B D

Hence, we proved

by SAS congruence criteria and

Therefore, the given statement is true.
So, option (1) is true.

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