wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Question 7
Using Basic proportionality theorem, prove that a line drawn through the mid-points of one side of a triangle parallel to another side bisects the third side.

Open in App
Solution


Given, ΔABC in which D is the mid-point 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 that E is the mid-point of AC.
Proof
D is the mid-point of AB.
AD=DB
ADBD=1...(i)
In ΔABC,DE||BC,
Therefore, ADDB=AEEC [By using Basic Proportionality Theorem]
1=AEEC [From equation (i)]
AE=EC
Hence, E is the mid-point of AC.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon