Question

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

Answer 1

16

Explanation:

Answer 2

Therefore AB is 16 units.

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=(1)/(2)AB` ..............Mid Point Theorem.

Substituting the values we get

`8=(1)/(2)AB\\\\AB=8* 2=16\ units`

Therefore AB is 16 units.