Question

in quadrilateral ACND.AC=AD bisects angle A show that ∆aABC=~ ∆ABD what can you say about BC and BD?​

Answer 1

Step-by-step explanation:

AC=AD (given)

AB=AB (common side)

angle BAC= angle BAD (AB is the angle bisector)

so by SAS we can say that triangles ABC is congruent to triangle ABD

so BC=BD

Answer 2

Step-by-step explanation:

Given :-

In a quadrilateral ACBD.

AC=AD

AB bisects angle A

To find :-

Show that ∆ABC=~ ∆ABD.

what can you say about BC and BD?

Solution :-

Given that

ACBD is a quadrilateral.

AC = AD

AB bisects angle A

Now , we have

∆ ABC and ∆ ABD

From ∆ ABC and ∆ ABD

AC = AD (Given )

< CAB = < DAB ( AB bisects angle A)

AB = AB ( Common side )

By SAS property

∆ ABC and ∆ ABD are congruent triangles.

∆ABC=~ ∆ABD.

Hence, Proved.

We know that

Corresponding parts in the Congruent triangles are equal.

=> BC = BD

Answer:-

∆ABC=~ ∆ABD.

BC = BD

Used formulae:-

SAS Property :-

→ In two triangles, The two sides and the included angle in a first triangle are equal to the corresponding two sides and the included angle in another triangle then they are congruent and this property is called Side - Angle - Side property.

→ Corresponding parts in the Congruent triangles are equal (CPCT).