1. Lesson 8-R
Chapter 8 Review

2. Objectives
Review Chapter 8: Similarity

3. Vocabulary
None new

4. Ratios and Proportions
Proportion is two ratios set equal to each other
Scaling Factor is a Ratio
Used in recipes to increase (sf > 1) or decrease (sf < 1) amount it makes
Top
Bottom
x + 2
--- =  14 = 7  (x + 2)
56 = 7x + 14
42 = 7x
6 = x
cross-multiply to solve
(remember distributive property with + or -)

5. Similar Polygons
Similar Polygons have the same shape and are different sizes based on the scaling factor (called in chapter 9, dilations – a transformation not )
Like with congruent triangles – Order Rules!
Trapezoid HJLJ ~ Trapezoid ACDB
so side HJ goes with AC
Remember to separate the variables
with the key (constant ratio)
= and =
t r - 3 A B C D 12 10 8 T H K J L 16
t + 3
r - 3 B

6. Triangle Similarity Theorems
Picture
Check
SSS
Only 3 sides given
All three sides have the same ratios
SAS
Two sides have the same ratios and the included angle is congruent AA
Two angle are congruent A B C D F E 5 4 3 9 12 15 A B C D F E 5 4 12 15 A B C D F E

7. Parallel Lines and Proportions
Parallel lines cut the sides of a triangle (or sides of two lines) into the same ratio
AB AC so = in ∆AED to the right BE CD A B C E D T B J N M K L 9 7 20
KL is a midsegment, which means K and L are midpoints and ∆JKL is half of ∆JMN B C A N P M
3x - 7
17 – x
y + 6 3y
If we have more than one variable,
then look for congruent marks;
otherwise, we can’t solve it.

8. Parts of Similar Triangles
If two triangles are similar then all parts of the triangles (perimeter, medians, altitudes, etc) have to be in the same ratio as the two triangles A B C D P Q R S 6 y 18 24 4
∆ABC ~ ∆PRQ T B
Side AB matches to side PR and gives
a 1 : 3 ratio. So y is
3 times 4 or 12. All parts
of ∆PRQ are 3 times larger
than corresponding parts
of ∆ABC
Reminder PS and AD are altitudes

9. Angle Bisector Theorem
An angle bisector cuts the side opposite in the same ratio as the sides that form the original angle.
x x + 3
--- =  (x + 3) = 6  x
4x + 12 = 6x
12 = 2x
6 = x J K L M 6 x 4
x + 3 B T
The Ratio of JL to JK must be the same as ML to MK

10. Summary & Homework Summary: Homework: Study for Ch 8 Test
Cross-multiply to solve proportions
Remember the distributive property
Order rules for matching corresponding sides of similar figures like congruent triangles
Parallel lines cut into equal ratios
All parts of similar triangles have the same ratio
Angle bisector cuts divided side into same ratio as the sides forming the angle
Homework: Study for Ch 8 Test