1. Similar Polygons Objectives: 1) To identify similar polygons
2) To apply similar polygons.

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

3. 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

4. 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!!

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

6. 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

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

9. 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.

10. 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.

11. 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?

12. Golden Rectangle – Is a rectangle that can be divided into a square and a rectangle that is similar to the original rectangle.
Pleasing to the eye.
In Architecture since the Greeks.
Da Vinci (1452 – 1519)
Divine Proportion: A book about the golden ratio.
Golden Ratio: :1

13. The golden rectangle R, constructed by the Greeks, has the property that when a square is removed a smaller rectangle of the same shape remains. Thus a smaller square can be removed, and so on, with a spiral pattern resulting.
                                                                                                                                                                                    
The Greeks were thus able to see geometrically that the sides of R have an irrational ratio, 1 : x. The smaller rectangle has sides with ratio 1-x : 1; since this is the same as the ratio for the big rectangle, one finds that x^2 = x+1 and thus x = (1+Sqrt(5))/2 =

14. GOLDEN RATIO = 1.618
The Golden Section is also known as the Golden Mean, Golden Ratio and
Divine Proportion. 
It is a ratio or proportion defined by the number Phi (   = )
It can be derived with a number of geometric constructions,
each of which divides a line segment at the unique point where:
the ratio of the whole line (A) to the large segment (B)
is the same as
the ratio of the large segment (B) to the small segment (C).
                                                                                             
In other words, A is to B as B is to C.
This occurs only where A is times B and B is times C.