### In a triangle, ABC, D is a point on AB such that AB = 4AD and E is a point on AC such that AC = 4AE. Prove that BC = 4ED.

**Answer:**

**Step by Step Explanation:**

- It is given in the question that D and E are the points on side AB and BC of ΔABC respectively. Join DE.
**Given:-**AB = 4AD

or, AD =

AB1 4

AC = 4AE

or, AE =

AC1 4 - We need to prove that the ΔADC and ΔABC are similar.

Where, A is the common angle in ΔADE and ΔABC.

Therefore,

=AD AB AE AC **[By BPT theorem.]**

Then,

=AD AB

=AE AC

------(1)ED BC

So, ΔABC ∼ ΔADE**[By SAS criteria.]** - As,

=AD AB

------(2)1 4

and

=AE AC

------(3)1 4 - On comparing (1), (2) and (3), we get:

=ED BC 1 4 - Hence, BC = 4ED.