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# In a ΔABC, D and E are points on the sides AB and AC respectively. For each of the following cases show that DE ∥ BCAB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm, and AE = 1.8 cm.

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Question drawn from very renowned book RD sharma of class 10th, Chapter no. 4
Chapter name:- Triangles
Exercise :- 4.2
This is very important question of triangle.

We have been given a triangle ΔABC,

In which D and E are points on the sides AB and AC respectively.

Now For following case we have to show that DE ∥ BC

Also it is given that AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm, and AE = 1.8 cm.

learning CBSE maths in efficient way

RD sharma, DHANPAT RAI publication
Class 10th, triangle

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### 1 Answer

1. Given:

Length of side AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm, and AE = 1.8 cm

To show : Side DE is parallel to BC ( DE || BC )

Now,

Length of side BD = AB – AD = 5.6 – 1.4 = 4.2 cm

And,

Length of side CE = AC – AE = 7.2 – 1.8 = 5.4 cm

Now,

AD/BD = 1.4/4.2 = 1/3                          – equation 1

AE/CE = 1.8/5.4 =1/3                              – equation 2

Now from equation 1 and 2

AD/BD = AE/CE

So, by the converse of Thale’s Theorem

We get, DE ∥ BC.

Hence, Proved.

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