CBSE Class 9 Answered
Prove that the line drawn through the mid point of one side of a triangle, parallel to another side, intersects the third side at its mid point.
Asked by Topperlearning User | 11 Aug, 2017, 12:00: PM
![](https://images.topperlearning.com/topper/questions/8812_image012.gif)
ABC is a triangle;
D is the mid point of AB.
To prove that E is the mid point of AC.
Let F be the mid point of the side AC and not the point E.
Join DF
In
ABC, D is the mid point of AB and DE
BC
![](https://images.topperlearning.com/topper/questions/8812_image002.gif)
![](https://images.topperlearning.com/topper/questions/8812_image003.gif)
F is the mid point of AC,
![](https://images.topperlearning.com/topper/questions/8812_image004.gif)
DF
BC, also DE
BC
![](https://images.topperlearning.com/topper/questions/8812_image003.gif)
![](https://images.topperlearning.com/topper/questions/8812_image003.gif)
Thus two intersecting lines DE and DF are parallel to the same line BC
This is not possible.
So F can not be the mid point of AC.
Hence, E is the mid point of AC.
Answered by | 11 Aug, 2017, 14:00: PM
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