Premium Online Home Tutors
3 Tutor System
Starting just at 265/hour
Answer :
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.
We have to prove that E is the mid point of AC.
Since, D is the mid-point of AB.
AD=DB
=>\(\frac{AD}{DB}\) = 1 …………………………. (i)
In \(\triangle ABC\), DE || BC,
By using Basic Proportionality Theorem,
Therefore, \(\frac{AD}{DB} = \frac{AE}{EC}\)
From equation (i), we can write,
=> 1 = \(\frac{AE}{EC}\)
=> AE = EC
Hence, proved, E is the midpoint of AC.