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. (Recall that you have proved it in Class IX).

Class 10 - Math - Triangles Page 129

Answer 1

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: E is the mid point of AC.


Proof: D is the mid-point of AB.

∴ AD=DB

⇒ AD/BD = 1 ... (i)

In ΔABC, DE || BC,

Therefore, AD/DB = AE/EC [By using Basic Proportionality Theorem]

⇒1 = AE/EC [From equation (i)]
∴ AE =EC
Hence, E is the mid point of AC.

Answer 2

Answer:

PQ is a line segment drawn through midpoint P of line AB such that PQ||BC

i.e. AP = PB

Now, by basic proportionality theorem

AQ/ QC = AP/PB

AQ/QC = 1/1

i.e. AQ = QC

Or, Q is midpoint of AC

HENCE PROVED