In a ΔABC, D and E are points on the sides AB and AC respectively. For each of the following cases show that DE ∥ BC:AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm, and AE = 2.8 cm.

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Asked: August 14, 20212021-08-14T15:31:00+05:30 2021-08-14T15:31:00+05:30In: CBSE

Question taken from RD sharma
Class 10th
Chapter no. 4
Chapter name:- Triangles
Exercise :- 4.2
This is very basic and important questions.

We have been given that in ΔABC, D and E are points on the sides AB and AC respectively

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

It is given that AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm, and AE = 2.8 cm.

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AAREKH · Answer 1 · 2021-08-19T00:23:03+05:30

Given:

Length of side AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm, and AE = 2.8 cm.

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

Now,

Length of side AD = AB – DB = 10.8 – 4.5 = 6.3

And,

Length of side CE = AC – AE = 4.8 – 2.8 = 2

Now,

AD/BD = 6.3/ 4.5 = 2.8/ 2.0 = 7/5 – equation 1

AE/CE = 7/5 – 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