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 1

⠀⠀ıllıllı uoᴉʇnloS ıllıllı

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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)

Therefore:

∆ ABC ≅ ∆ABD (By SAS congruence axiom)

Therefore:

• BC = BD (By CPCT)

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Answer 2

Hey mate!

Here is your answer!

Given:

AC = AD... (1)

AB bisects <A

i.e <CAB = <DAB... (2)

To prove:

TRI ABC = TRI ABD

Proof:

In TRI ABC and TRI ABD,

AB = AB (common)

<CAB = <DAB (from... 2)

AC = AD (from... 1)

Therefore, TRI ABC = TRI ABD (SAS congruence rule)

Therfore, BC = BD (CPCT)

Therefore, BC, BD are of equal length.

Hope you got it!

P. S TRI means triangle symbol.