E is the mid-point of a median AD of ∆ABC and BE is produced to meet AC at F. Show that AF = 1/3 AC.
Solution:
Given, ABC is a triangle
E is the midpoint of a median AD
BE is produced to meet AC at F
We have to show that AF = 1/3 AC
Draw DP parallel to EF
Considering triangle ADP,
E is the midpoint of AD
EF || DP
By converse of midpoint theorem,
F is the midpoint of AP.
Considering triangle FBC,
D is the midpoint of BC
DP || BF
By converse of midpoint theorem,
P is the midpoint of FC
So, AF = FP = PC
Therefore, AF = 1/3 AC
✦ Try This: In the adjacent figure, ar(PEA) = ar(PAC) and ar(RPC) = ar(KEA) show that quadrilateral PARK and PACE are trapezium.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 8
NCERT Exemplar Class 9 Maths Exercise 8.4 Problem 10
E is the mid-point of a median AD of ∆ABC and BE is produced to meet AC at F. Show that AF = 1/3 AC.
Summary:
E is the mid-point of a median AD of ∆ABC and BE is produced to meet AC at F. It is shown that AF = 1/3 AC by the converse of midpoint theorem which states that if a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side
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