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).
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10th
Maths
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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VIDEO EXPLANATION
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
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.