Question

In a quadrilateral ABCD. AB= AD and AC is bisector angleA` show that ∆ ABC =~ ∆ ABD​

Answer 1

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)

Answer 2

Answer:

Step-by-step explanation:

in triangle abc & abd

AB = AD (GIVEN)

<BAC = <DAC (AC IS BISECTOR OF A)

AC = AC   (COMMON)