Question

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

Answer 1

Answer:

Congruence of triangles:

Two ∆’s are congruent if sides and angles of a triangle are equal to the corresponding sides and angles of the other ∆.

 

In Congruent Triangles corresponding parts are always equal and we write it in short CPCT i e, corresponding parts of Congruent Triangles.

 

It is necessary to write a correspondence of vertices correctly for writing the congruence of triangles in symbolic form.

 

Criteria for congruence of triangles:

There are 4 criteria for congruence of triangles.

In this question we use SAS

SAS( side angle side):

Two Triangles are congruent if two sides and the included angle of a triangle are equal to the two sides and included angle of the the other triangle.

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Solution:

 

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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Answer 2

Answer:

Hope It helped,

Step-by-step explanation:

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