Question

In Fig. 10.92, it is given that AB = CD and AD = BC. Prove that Δ ADC ≅ Δ CBA.

Answer 1

Step-by-step explanation:

AB = CD

And,

AD = BC

To prove: Δ ADC ≅ Δ CBA

Proof: Consider,

AB = CD (Given)

BC = AD (Given)

AC = AC (Common)

By SSS theorem,

Δ ADC ≅ Δ CBA

Hence, proved

Answer 2

Concept :  

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.

 

 

 

Given : AB = CD and AD = BC.  

To Prove : Δ ADC ≅ Δ CBA.

Proof:  

In Δ ADC and Δ CBA , we have

AB = CD (Given)

BC = AD (Given)

AC = AC (Common)

Δ ADC ≅ Δ CBA

[By SSS congruence criterion]

Hence, proved

HOPE THIS ANSWER WILL HELP YOU…..

 

 

Some questions of this chapter :

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that (i) ABE ≅ ACF (ii) AB = AC, i.e., ABC is an isosceles triangle.

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AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠BAD = ∠ABE and ∠EPA = ∠DPB (See the given figure). Show that (i) ΔDAP ≅ ΔEBP (ii) AD = BE

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