Question

In the adjoining figure, AC = AE , AB= AD and Angle BAD = Angle CAE. Show that BC = DE.
plz answer this question ASAP ​

Answer 1

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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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Solution:

First show that ΔABC ≅ ΔADE by using SAS rule

and then use  CPCT  to show given result.

 

Given,

AC = AE, AB = AD and ∠BAD = ∠EAC

 

To prove:

BC = DE

Proof: We have

∠BAD =

∠EAC

(Adding ∠DAC to both sides)

∠BAD +

∠DAC =

∠EAC +

∠DAC

⇒ ∠BAC = ∠EAD

In ΔABC and ΔADE,

AC = AE (Given)

∠BAC =

∠EAD                    (proved

above)

AB = AD                                   (Given)

Hence, ΔABC ≅ ΔADE             (by SAS congruence rule)

Then,

BC = DE                                      ( by CPCT.)

 

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