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.
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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 = AB
AC = 4AE
or, AE = AC
- We need to prove that the ΔADC and ΔABC are similar.
Where, A is the common angle in ΔADE and ΔABC.
Therefore, = [By BPT theorem.]
Then, = = ------(1)
So, ΔABC ∼ ΔADE [By SAS criteria.]
- As, = ------(2)
and = ------(3)
- On comparing (1), (2) and (3), we get:
- Hence, BC = 4ED.