Question

Question of class - 9
Don't use Basic Proportionality Theorem

Find AE= ?
Given =>AP=2PC

Answer 1

G.T: AP=2PC
1/2AP=PC
AP=2×3=6 -(1)
[given that PC= 3cm]

D is the m.p of AB
given that: DE||BP
by using converse of m.p theorem..
E is the m.p of AP
AE =1/2 AP
AE= 1/2×6
=3.

Answer 2

given ,

AD = DB = 4cm
PC = 3cm

AP = 2PC

Now
AD = DB [each 4 cm]
therefore
D is the midpoint of AB
and DE ll BP [given]
therefore ,
E is the midpoint of AP
[converse midpoint theorem]
so,
AE = 1/2 AP
= 1/2(2PC) [ AP = 2PC]
= PC
= 3 cm