1. Objective
•Students will prove
and apply the side-
splitter theorem and
other similarity
properties.

2. Side-splitter Theorem
• A line parallel to one
side of a triangle
divides the other two
sides proportionally

4. Use the side-splitter
to solve for x and y:
18
6
y 6
x

5. Check It Out! Example 1
Find PN.
Use the Triangle Proportionality
Theorem.
Substitute in the given values.
2PN = 15 Cross Products Prop.
PN = 7.5 Divide both sides by 2.

7. Example 2: Verifying Segments are Parallel
Verify that .
Since , by the Converse of the Triangle Proportionality
Theorem.

8. Check It Out! Example 2
AC = 36 cm, and BC = 27 cm. Verify
that .
Since , by the Converse of the
Triangle Proportionality Theorem.

9. Two Transversal
Proportionality Corollary
• Two or more parallel lines
divide two transversals
proportionally
a c a
= c
b d b
d

11. So, you might want
to I askx?
• Can find
yourself:
• NO YOU MUST KNOW
LINES ARE //
5 x
9
3

12. Solve for y
4x
5x
3x
15

13. Triangle Angle-Bisector
Theorem
• If a ray bisects an angle of a
triangle then it divides the
opposite side into segments
proportional to the other two sides

14. The previous theorems and corollary lead to the following conclusion.

15. Example 4: Using the Triangle Angle Bisector Theorem
Find PS and SR.
by the ∆ Bisector Theorem.
x = 30
PS = x – 2 SR = x + 5
= 30 – 2 = 28 = 30 + 5 = 35