1. Similarity Solve for x. 4. 5. 6. X=6 X=-3, -3 X=16.5
Determine if the following pairs of ratios are equivalent (try using a different method on each one).
Solve for x. 4. 5. 6.
X=6
X=-3, -3
X=16.5

2. What does it mean for a set of figures to be
SIMILAR ?

3. What You Will Learn
Use similarity statements.
Find corresponding lengths in similar polygons.
Find perimeters and areas of similar polygons.
Decide whether polygons are similar.

4. Dr. Evil and Mini-Me

5. This memorial to Crazy Horse is still in the process of being carved
This memorial to Crazy Horse is still in the process of being carved. It was started 55 years ago. When finished, Crazy Horse will be 641 feet long and will stand 563 feet high.
                                                                                                                          
How do they know what the size will be if they haven’t finished carving it?

6. Each face of the four presidents displayed on Mount Rushmore is 60 feet high.

7. How do they know what dimensions to use for each face?

8. Similarity can be used to reduce something into a smaller, more manageable size, or enlarge something into a larger size so that it can be viewed more easily. This is done using the properties of dilation or proportion.
enlarging a cell
blueprints for a house
looking at a globe

9. SIMILAR FIGURES HAVE…
Proportional sides - corresponding sides are dilated by the same scale factor or have the same similarity ratio.
Congruent angles – corresponding sides have equal measures
The Scale Factor is

10. Similar Polygons Corresponding Parts:
∆ABC ~ ∆DEF is read “triangle ABC is __________________ to triangle DEF”.
Corresponding angles: Ratios of corresponding side lengths:
In the diagram, △RST ∼ △XYZ.
a. Find the scale factor from △RST to △XYZ.
b. List all pairs of congruent angles.
c. Write the ratios of the corresponding side
lengths in a statement of proportionality.

11. SIMILAR -Proportional Sides Find the missing side using proportion.

12. SIMILAR -Proportional Sides Find the missing side using proportion
SIMILAR -Proportional Sides Find the missing side using proportion. Find y.

13. Find the Scale Factor given ∆LMN ~ ∆ RST
M S 7
L N T R
What is the scale factor if ∆LMN is dilated to ∆RST?
A 16/15 B 4/5 C 5/4 D 1.5

14. Similar – Perimeter The triangles are similar. Find the perimeter
of ∆ HNK.
A 24unit B 40units C 30 units D units
Can you find the answer more than one way?

15. Theorem 8.1: If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.
Practice

17. What properties should these figures have to be considered similar?

18. Similar or Not Similar that is the question?
Really?