Question

In quadrilateral ABCD,
AC= AD and AB bisects angle A show that ABC is congruent to ABD.
What can you say about BC and BD.

plz give proper answer step by step written.



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Answer 1

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Given: AC = AD and AB bisects ∠A

To Prove: Δ ABC ≅ Δ ABD

We can show two sides and included angle of ABC are equal to the corresponding sides and included angle of ABD.

In quadrilateral ACBD, AC = AD and AB bisects ∠A (see Fig. 7.16). Show that Δ ABC ≅ Δ ABD. What can you say about BC and BD?

In Δ ABC and Δ ABD,

AC = AD (Given)

∠CAB = ∠DAB (AB bisects ∠A)

AB = AB (Common)

∴ Δ ABC ≅ Δ ABD (By SAS congruence rule)

∴ BC = BD (By CPCT)

Therefore, BC and BD are of equal lengths !