Question

in a quadrilateral ABCD. AB=AD & AC bisects angle A show that triangle ABC congruent to triangle ABD


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Answer 1

Step-by-step explanation:

Proved bellow.

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Our question is: In a quadrilateral ABCD AB=AD and AC bisects angle A show that triangle ABC is congruence to triangle ABD.

We know that AB = AD and a bisector of angle A is AC. Our aim is to prove that ABD is congruent with ACD.

AC is a bisector of A, then:

⇒ ∠DAC = ∠BAC

In ΔADC and ΔABC, we know that AD=AB and ∠DAC=∠BAC, hence:

⇒ AC = AC

By SAS, if two triangles have two equal sides or congruent sides, and an equal angle formed by these sides, then both triangles are congruent.

Hence, ΔABD ≅ ΔACD.