Question

In quadrilateral ACBD, AC=AD and AB bisects angleA. Show that triangle ABC congruent to triangle ABD. What can you say about BC and BD
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Answer 1

Answer:

In quadrilateral ACBD, AC=AD and AB bisects angleA. Show that triangle ABC congruent to triangle ABD. What can you say about BC and BD.

Here is the solution:

Step-by-step explanation:

To prove :Triangle ABD congruent to triangle BCD.

AC =AD (Given) (side)

Angle CAB=Angle DAB (as the line AB is the bisector of angle A)

AB =AB (common side)

Therefore both the Triangles are congruent by SAS(side angle side) congruency.

Hence proved.

Answer 2

$\huge\textsf{Question:}$

In quadrilateral ACBD, AC=AD and AB bisects angleA. Show that triangle ABC congruent to triangle ABD. What can you say about BC and BD.

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$\LARGE\underline{\underline{\sf Solution:}}$

In Quadrilateral ACBD :-

To prove :-

∆ABC ≅ ∆ ABD

Proof :-

AC = AD (Given)

AB = AB (Common)

∠CAB = ∠DAB

∵ AB bisect ∠A

∴ ∠ABC ≅ ∠ABD (SAS Rule)

∴ BC = BD (C.P.C.T)

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