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.

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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First use, SAS rule to show congruence of triangles and then use CPCT to show ii & iii parts.

Given:

In quadrilateral ABCD,

AD = BC &

∠DAB = ∠CBA

To Prove:

(i) ΔABD ≅ ΔBAC

(ii) BD=AC

(iii) ∠ABD = ∠BAC

Proof:

i)

In ΔABD & ΔBAC,

AB = BA (Common)

∠DAB = ∠CBA (Given)

AD = BC (Given)

Hence, ΔABD ≅ ΔBAC.

( by SAS congruence rule).

(ii) Since, ΔABD ≅ ΔBAC

Then, BD = AC ( by CPCT)

(iv) Since, ΔABD ≅ ΔBAC

Then , ∠ABD = ∠BAC (by CPCT)

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Hope this will help you.....

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DiyaDebeshee

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in triangle ABD and triangle BAC

AB=BC (GIVEN)

∠DAB = ∠ CBA (GIVEN)

AB = BA (COMMON)

THEREFORE, TRIANGLE ABD ≅ TRIANGLE BAC ( BY SAS)

THEREFORE, BD = AC (CPCT)

ALSO, ∠ ABD = BAC (CPCT)

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hope it is helpful

@ debeshee

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