Using Converse of basic proportionality theorem, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.

Asked by Pragya Singh | 1 year ago |  49

#### 1 Answer

##### Solution :-

Given, in ΔABC, D and E are the mid points of AB and AC respectively, such that,

AD=BD and AE=EC.

We have to prove that: DE || BC.

Since, D is the midpoint of AB

AD=DB

$$\dfrac{AD}{BD}$$ = 1……………………………….. (i)

Also given, E is the mid-point of AC.

AE=EC

⇒ $$\dfrac{AE}{EC}$$ = 1

From equation (i) and (ii), we get,

$$\dfrac{AD}{BD}$$ = $$\dfrac{AE}{EC}$$

By converse of Basic Proportionality Theorem,

DE || BC

Hence, proved.

Answered by Abhisek | 1 year ago

### Related Questions

#### In an trapezium ABCD, it is given that AB ∥ CD and AB = 2CD. Its diagonals AC and BD

In an trapezium ABCD, it is given that AB ∥ CD and AB = 2CD. Its diagonals AC and BD intersect at the point O such that ar(∆AOB) = 84 cm2. Find ar(∆COD)

Class 10 Maths Triangles View Answer

#### Find the length of the altitude of an equilateral triangle of side 2a cm.

Find the length of the altitude of an equilateral triangle of side 2a cm.

Class 10 Maths Triangles View Answer

#### A ladder 10 m long reaches the window of a house 8 m above the ground.

A ladder 10 m long reaches the window of a house 8 m above the ground. Find the distance of the foot of the ladder from the base of the wall.

Class 10 Maths Triangles View Answer

#### In the given figure, DE ∥ BC such that AD = x cm, DB = (3x + 4) cm, AE = (x + 3) cm

In the given figure, DE ∥ BC such that AD = x cm, DB = (3x + 4) cm, AE = (x + 3) cm and EC = (3x + 19) cm. Find the value of x.

Class 10 Maths Triangles View Answer

#### If ∆ABC ∼ ∆DEF such that 2 AB = DE and BC = 6 cm, find EF.

If ∆ABC ∼ ∆DEF such that 2 AB = DE and BC = 6 cm, find EF.

Class 10 Maths Triangles View Answer