In the figure below, F is between E and G , and G is between F and H. if FH13, FG=5, and EG=9, find EH

Answer 1

There is no figure...

I assume that

E----- F------- G-------------- H

FH = 13, FG = 5, EG = 9

then,

By Segment Addition Postulate,

EG = EF + FG

9 = EF + 5

EF = 4

Now, EH = EF + FH = 4 + 13 = 17 , by Segment Addition Postulate.

EH = 17

Answer 2

Presuming that all the points given are in sequence on a line,

EG= EF+ FG

Substuting the given values for both EG and FG,

9 = EF + 5

Subtracting 5 from both sides of the equation,

4 = EF

or, using the symmetric property of equality (if a = b, then b = a),

EF = 4.

EH = EF + FH = 4 + 13 = 17

The Line Segment Addition Postulate states that the length of a line is equal to the sum of its component parts.

A postulate, by the way, is something that cannot be proven as strongly as a theorem. It is more than just an assumption, however. It can be viewed as a "self-evident truth".