1. Similar Polygons
Circle Limit III
M.C. Escher

2. Figures that are similar (~) have the same shape but not necessarily the same size.

3. Similar figures look alike but one is a smaller
version of the other.
It wouldn’t make much sense to make a drawing
of this ship the actual size of the ship.

4. All the angles are the same All sides are proportional
Two polygons are similar polygons if and only if their corresponding angles are congruent & their corresponding side lengths are proportional.
All the angles
are the same
All sides are
proportional

5. Similar Polygons – 2 polygons that have the same shape but not the same size.
Symbol ( ~ )
Corresponding s are .
Corresponding sides are Proportional.
Equal Ratios:
** Reduce to the same fraction!!

6. Writing a similarity statement is like writing a congruence statement—be sure to list corresponding vertices in the same order.
Writing Math

7. Ex: Order Matters ΔABC ~ ΔXYZ 4 6 = AB = 15 10 AB 4 8 = AC = 20 10 AC
78 4 6
BC corresponds to YZ B
42 Z X 8 10
Find AB: 4 6 =
AB = 15 10 AB A C 4 8 =
mB =
mC = 78 60
AC = 20
Find AC: 10 AC

9. Example : Identifying Similar Polygons
Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement.
rectangles ABCD and EFGH

10. Example 3
A boxcar has the dimensions shown.
A model of the boxcar is 1.25 in. wide. Find the length of the model to the nearest inch.

11. Example 3 Continued
1.25(36.25) = x(9)
Cross Products Prop.
45.3 = 9x
Simplify.
5  x
Divide both sides by 9.
The length of the model is approximately 5 inches.

12. Ex. 2: Are the following polygons similar?B C
120
1in K L
1in
4in
4in
2in
2in
80 J M
1in A D
2in
Check to see if all s are ?
Check the ratio of all corresponding sides?