1. Ratios and Proportions
Geometry
Unit 11, Day 1
Ms. Reed

2. Review: Solve for x
= x
= x

3. Similar Figures Figures are similar if
Corresponding angles are congruent
Corresponding sides are proportional
The ratio of the corresponding sides is called the similarity ratio

4. Find the Similarity Ratio:B C D E F
AB = BC = AC = DE EF DF
We can now say ΔABC ~ ΔDEF
The similarity ratio is 1/2
Similarity Statement

5. ΔXYZ ~ ΔMNP with a similarity ratio of 1/3
Example: Write a similarity statement and give the similarity ratio of the following: 42 P N Y 14 48 12 36 X Z 16 M
ΔXYZ ~ ΔMNP with a similarity ratio of 1/3

6. Proportions Proportion – a statement of two equal ratios
a = c OR a : b = c : d b d

7. Extended Proportion
An extended proportion can be written when 3 or more ratios are equal.
18 = 15 =

8. Are the polygons similar? #1
If the polygons are similar write a similarity statement and give the similarity ratio.
E F 30
H G
A B 20
D C 36 52
NOT SIMILAR

9. Are the polygons similar? #221
W X
Y Z
A B
C D 14 6 6 4 4 9 6
ABCD ~ WXYZ with a similarity ratio of 2/3

10. Leaning Tower of Pisa
The Leaning Tower of Pisa in Italy is about 180 ft tall. A souvenir paperweight of the Leaning Tower is 6 in. tall. What is the similarity ratio of the paperweight to the real tower?

11. Practice Find the value of all the variables if ΔABC ~ ΔDEF
w = 21 x = 101° y = 27° z = 12 B E z 8 x° 9 6
27°
52° y° A D F C w 28