Question

in quadrilateral acbd ac=ad and ab bisects angle a show that triangle abc is congruent to triangle abd what can you say about bc and bd​

Answer 1

SHORT ANSWER:

In △ABC and △ABD,

AC=AD (Given)

∠CAB=∠DAB (AB bisects ∠A)

AB=AB (Common)

∴△ABC≅△ABD (By SAS congruence rule)

∴BC=BD (By CPCT)

∴, BC and BD are equal.

LONG 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.

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.

Answer 2

I know but you should solve it your own way