1. Drill Find x, if the semicircle arc of a circle is 3x + 30 degrees.
a. 4/6 = x/18
b. 2/x = 10/15
3) If the radius of a circle is 3x + 4 and the diameter is 5x + 16 what is the the radius of the circle?

2. Chapter 2
Geometric Figures

3. 2.6 Congruent and Similar Figures

4. Vocabulary (1) corresponding angles are congruent.
Similar: two polygons are similar if:
(1) corresponding angles are congruent.
(2) corresponding sides are proportional.
(3) All sides are multiplied by the same scale factor (#)

5. Similar Polygons G F H E AB AB BC CD DA = = = = EF FG GH HE

6. Ex. 1: Writing Similarity Statements
Pentagons JKLMN and STUVW are similar. List all the pairs of congruent angles. Write the ratios of the corresponding sides in a statement of proportionality.

7. Ex. 1: Writing Similarity Statements
Because JKLMN ~ STUVW, you can write J  S, K  T, L  U,  M  V AND N  W.
You can write the proportionality statement as follows: JK KL LM MN NJ = = = = ST TU UV VW WS

8. Ex. 2: Comparing Similar Polygons
Decide whether the figures are similar. If they are similar, write a similarity statement.

9. So, the two figures are similar and you can write WXYZ ~ PQRS.
SOLUTION:
As shown, the corresponding angles of WXYZ and PQRS are congruent. Also, the corresponding side lengths are proportional. WX 15 3 = = PQ 10 2 YZ 9 3 XY 6 3 = = = = RS 6 2 QR 4 2 WX 15 3 = =
So, the two figures are similar and you can write WXYZ ~ PQRS. PQ 10 2

10. Ex. 3: Comparing Photographic Enlargements
POSTER DESIGN. You have been asked to create a poster to advertise a field trip to see the Liberty Bell. You have a 3.5 inch by 5 inch photo that you want to enlarge. You want the enlargement to be 16 inches wide. How long will it be?

11. Solution:
To find the length of the enlargement, you can compare the enlargement to the original measurements of the photo.
16 in.
x in. = 5
3.5 in.
5 in. 16
3.5
∙ 5 x =
3.5
x ≈ 22.9 inches
The length of the enlargement will be about 23 inches.

12. Using similar polygons in real life
If two polygons are similar, then the ratio of lengths of two corresponding sides is called the scale factor. In Example 2 on the previous page, the common ratio of is the scale factor of WXYZ to PQRS. 3 2

13. Ex. 4: Using similar polygons
The rectangular patio around a pool is similar to the pool as shown. Calculate the scale factor of the patio to the pool, and find the ratio of their perimeters.
16 ft
24 ft
32 ft
48 ft

14. The ratio of the perimeters is
Because the rectangles are similar, the scale factor of the patio to the pool is 48 ft: 32 ft. , which is 3:2 in simplified form.
The perimeter of the patio is 2(24) + 2(48) = 144 ft. and the perimeter of the pool is 2(16) + 2(32) = 96 ft.
The ratio of the perimeters is
16 ft
24 ft
32 ft
48 ft
144 3
, or 96 2

15. Ex. 5: Using Similar Polygons
Quadrilateral JKLM is similar to PQRS. Find the value of z.
Set up a proportion that contains PQ
Write the proportion.
Substitute
Cross multiply and divide by 15. KL JK = QR PQ 15 10 = 6 Z
Z = 4

16. Homework
Pages 105 – 106
#’s 1 – 8, 12, 16, 20, 26
#’s 32, 34, 36, 40