Question

[By converse of B.P.IT
ole parallel to another
BC II QR
Using B.P.T., prove that a line drawn through the mid-point of one side of a triangle parallel to
side bisects the third side.
he mid.noint of AB and DE || BC​

Answer 1

Answer:

statement:

A straight line drawn parallel to a side of a triangle intersecting the other two sides ,divides the sides in the same ratio

Given:

In triangle ABC, D is a point on AB and E is a point on AC .

To prove:

AD/DB = AE/EC

Construction:

Draw DE || BC

Proof:

In triangle ABC and ADE

angle ABC = angle ADE ( CORESSPONDING ANGLES ARE EQUAL BECAUSE DE|| BC)

angle DAE= angle BAC ( COMMON ANGLE A)

angleACB=. angle AED (CORESSPONDING ANGLES ARE EQUAL BECAUSE DE|| BC)

by AAA similarity

triangle ABC ~triangleADE

AB/AD= AC/AE

AD+DB/AD=AE+EC/AE

1+DB/AD= 1+ EC/AE

DB/AD= EC/AE (CANCELLING 1 ON BOTH SIDES)

AD/DB= AE/EC ( TAKING RECIPROCAL ON BOTH SIDES)

HENCE PROVED

Mark me the brainliest answer plz

Answer 2

Given,In triangle ABC, D is the midpoint of AB such that AD=DB.

A line parallel to BC intersects AC at E as shown in above figure such that DE||BC.

To prove, E is the midpoint of AC.

Since, D is the midpoint of AB

So,AD=DB

⇒ AD/DB=1.....................(i)

In triangle ABC,DE||BC,

By using basic proportionality theorem,

Therefore, AD/DB=AE/EC

From equation 1,we can write,

⇒ 1=AE/EC

So,AE=EC

Hence, proved,E is the midpoint of AC.