1. GT Geom 3/11/14
• Turn in CW/HW from yesterday on the
book shelf.
• Pass out papers in the bin. If you turn
something into me it should have a grade
on when you get it back. If you don’t turn
it in to me you don’t get a grade.

2. Given
Prove
RSPQ//
QT
SQ
PT
RP

R
P
T
Q
S

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

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

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

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

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

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

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

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

14. Solve for x
5x
15
3x
4x

15. 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

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

17. 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