Question

5. In the adjoining figure, if AD/DC = BE/EC and angleCDE = angleCED Prove that triangleCAB is isosceles.

Standard:- 10th

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Answer 1

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Given : ∆CAB in which AD/DC = BE/EC and
angle CDE = angle CED ------ (1)

To Prove : ∆CAB is isosceles

Proof : Here if AD/DC = BE/EC, by Converse of BPT,

=> DE II AB

Thus

=> angle CDE = angle A -------(2)

=> angle CED = Angle B -------(3)

From (1) , (2) and (3)

=> angle A = angle B

Thus

=> AC = BC (side opposite equal angles)

Thus ∆CAB is an isosceles triangle

Hence Proved

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Answer 2

Answer:

Step-by-step explanation:

Given : ∆CAB in which AD/DC = BE/EC and

angle CDE = angle CED ------ (1)

To Prove : ∆CAB is isosceles

Proof : Here if AD/DC = BE/EC, by Converse of BPT,

=> DE II AB

Thus

=> angle CDE = angle A -------(2)

=> angle CED = Angle B -------(3)

From (1) , (2) and (3)

=> angle A = angle B

Thus

=> AC = BC (side opposite equal angles)

Thus ∆CAB is an isosceles triangle

Hence Proved