### Stewart`s Theorem

```* In geometry, Stewart's Theorem is named in honor of
the Scottish mathematician Matthew Stewart. He
published this theorem in 1746. It is also known as
"Proposition II" in Stewart's book Some General
Theorems of Considerable Use in the Higher Parts of
Mathematics.
*
* Stewart's
theorem yields a relation between the lengths
of the sides of the triangle and the length of a cevian of
the triangle.
* A cevian is
a line segment or ray that extends from one
vertex of a polygon to the opposite side (or the
extension of that side). Medians, altitudes, and angle
bisectors are all examples of cevians.
* The theorem helps find the measure of any line segment
from the vertex of a triangle to the opposite side.
*
The theorem is
established from
Cosines law.
A
man + dad = bmb + cnc
b
c
“A man and his dad put a
bomb in the sink”
d
B
m
n
D
a
C
A
4
x
3
B
3
D
2
C
In right ∆ABC, AB is 4cm, AC is 3cm, BD is 3 cm, and DC is 2cm.
Using Stewart’s Theorem, what is the value of x?
E
Isosceles ∆EFG has a leg
measure of 10in. FH has 2in
and HG has 6in. Find x.
10
x
F
2
H
6
G
*
```