Math, asked by ashimkaghz, 8 months ago

5)
Prove that the line drawn from the mid-point of one side of a triangle parallel of another
side bisects the third
side. (Use Converse of BPT).​

Answers

Answered by supriyaprasad1544
1

Step-by-step explanation:

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Triangles

Basic Proportionality Theorem (Thales Theorem)

Using Theorem 6.1, prove th...

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Asked on October 15, 2019 by

Ruchita Abhijit

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.

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ANSWER

Given:

In △ABC,D is midpoint of AB and DE is parallel to BC.

∴ AD=DB

To prove:

AE=EC

Proof:

Since, DE∥BC

∴ By Basic Proportionality Theorem,

DB

AD

=

EC

AE

Since, AD=DB

EC

AE

=1

∴ AE=EC

solution

Answered by BlessedMess
0

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.

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