Question

C
A
B
D
Fig. 7.16
In quadrilateral ABCD,
AC = AD and AB bisects √A .show that ∆ABC ~= ∆ABD. what can you say about BC and BD?
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Answer 1

Answer:

Given: In quadrilateral ABCD,

AC = AD & AB bisects ∠A i.e, ∠CAB = ∠DAB

To prove,

ΔABC ≅ ΔABD

Proof,

In ΔABC & ΔABD,

AB = AB (Common)

AC = AD (Given)

∠CAB = ∠DAB (AB is bisector)

Hence, ΔABC ≅ ΔABD. (by SAS congruence rule)

Then, BC= BD (by CPCT)

Thus, BC & BAD are equal.

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Step-by-step explanation:

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Answer 2

Question :-

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

Answer :-

In quadrilateral ACBD, we have AC = AD and AB being the bisector of ∠A.

Now, In ∆ABC and ∆ABD,

AC = AD (Given)

∠ CAB = ∠ DAB ( AB bisects ∠ CAB)

and AB = AB (Common)

∴ ∆ ABC ≅ ∆ABD (By SAS congruence axiom)

∴ BC = BD (By CPCT)

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