Transcript Section 7.5

Theorem
If a line is
parallel to one
side of a
triangle and
intersects the
other two sides,
then it divides
those sides
proportionally.
If
Then
RS XY
XR YS

RQ SQ
Q
R
X
S
Y
Corollary
If a line is
parallel to one
side of a
triangle and
intersects the
other two sides,
then it divides
those sides
proportionally.
If
Then
a b c
ST XY

TU YZ
X
S
a
Y
Z
T
U
b
c

What is the value of x?
12
9

x 1 x
12x  9x  9
12
9
3x  9
x3
X+1
x

What are the values of x and y?
x
9
8
7.2
6.4
y
x
9

8 7.2
8 7.2

6.4
y
7.2x  72
8 y  46.08
x  10
y  5.76
Theorem
If a ray bisects an
angle of a triangle,
then it divides the
opposite side into
two segments that
are proportional to
the other two sides
of the triangle.
If
Then
AD bisects CAB
CD CA

DB BA
A
C
D
B

What is the value of x?
10 12

18 x
18
10
12
10x  216
X
x  21.6

P. 475 #’s 9-22, 24-30, 33-35, 44-45, 51-58