Question

AE = EC and BF = FC. EF = 8 and DF = 10. AB = [?]

Answer 1

Answer:

Therefore AB is 16 units.

Step-by-step explanation:

Given:

AE = EC

BF = FC

EF = 8 and DF = 10

To Find:

AB = ?

Solution:

Mid Point Theorem:

The Midpoint Theorem states that "the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side".

AE = EC .....Given

Therefore E is the Mid Point of AC.

BF = FC .....Given

Therefore F is the Mid Point of BC.

Therefore,

EF || AB            ........................Mid Point Theorem.

$EF=\dfrac{1}{2}AB$          ..............Mid Point Theorem.

Substituting the values we get

$8=\dfrac{1}{2}AB\\\\AB=8\times 2=16\ units$

Therefore AB is 16 units.