Using basic proportionality theorem, prove that a line drawn through the midpoint of one side of a triangle and parallel to another side bisects the third side.

Open in App

Solution

In $△ M N S$ , line KL $∥$ side NS .....(given)
$∴ \frac{M K}{K N} = \frac{M L}{L S}$ ..... (By BPT)
But $M K = K N$
$∴ \frac{M K}{K N} = 1$
$∴ \frac{M L}{L S} = 1$
$∴ M L = L S$
This means that line KL bisects side MS.

Suggest Corrections

Similar questions

Q. Question 7
Using Basic proportionality theorem, prove that a line drawn through the mid-points of one side of a triangle parallel to another side bisects the third side.

Using Basic proportionality theorem, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).

Q. Using Theorem

6.1,

prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).

Theorem 6.1: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

Q. Prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.

Q. Prove that a line draw through the mid point of one side of a triangle parallel to another side bisects the third side .

Join BYJU'S Learning Program

Using basic proportionality theorem, prove that a line drawn through the midpoint of one side of a triangle and parallel to another side bisects the third side.

In △MNS, line KL ∥ side NS .....(given)∴MKKN=MLLS ..... (By BPT)But MK=KN∴MKKN=1∴MLLS=1∴ML=LSThis means that line KL bisects side MS.

In $△ M N S$ , line KL $∥$ side NS .....(given)
$∴ \frac{M K}{K N} = \frac{M L}{L S}$ ..... (By BPT)
But $M K = K N$
$∴ \frac{M K}{K N} = 1$
$∴ \frac{M L}{L S} = 1$
$∴ M L = L S$
This means that line KL bisects side MS.