Question

In quadrilateral ACBD , AC=AD and AB bisect < . Show that

∆ ≅ ∆. What can you say about BC and BD.​
​

Answer 1

Step-by-step explanation:

in triangle ACB &ADB

AB = AB ( common side)

<B =<B ( angle is bisected by AB)

AC =AD (given)

:. triangle ACB=~ADB (SAS)

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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