Question

prove that a line drawn through the mid- point of one side of a triangle parallel to another side bisects the third side​

Answer 1

Given :-

● Let takes the triangle ABC

● DE is parallel to BC

● D is the midpoint of AB

To prove :-

E is the midpoint of AC

Proof :-

In ΔABC

As it already given in the question that,

DE || BC

Therefore,

AD / DB = AE / EC

[ If a line 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 ]

As we know that,

DB = AD [ D is the mid point of BD ]

Therefore,

DB/DB = AE / EC

1 = AE / EC

EC = AE

Hence, E is the midpoint of AC$.$

Answer 2

Answer:

$\huge \underline \mathfrak \red{Solution}$

Given :-

▶ Let takes the triangle ABC

▶ DE is parallel to BC

▶ D is the midpoint of AB

To prove :-

E is the midpoint of AC

Proof :-

In ΔABC

As it already given in the question that,

DE || BC

Therefore,

AD / DB = AE / EC

[ If a line 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 ]

As we know that,

DB = AD [ D is the mid point of BD ]

Therefore,

DB/DB = AE / EC

1 = AE / EC

EC = AE

Hence, E is the midpoint of AC