Entry Task

7-2 Similar Polygons

Read the first page of the handout about Similar Polygons. Then answer the following questions and discuss with a partner.  What does it mean if two figures are similar?  What does it mean if two figures are congruent?  Are all rectangles similar? What about circles, squares, and triangles?

Investigation 1  Do the investigation on the back page of the handout.  You will need patty paper and a ruler.  Answer the questions in steps 1-3 in your notes.  How do the corresponding angles compare?  How do the ratios of the corresponding sides compare?

Definition of similar polygons  Two polygons are similar if and only if the corresponding angles are congruent and the corresponding sides are proportional.  So what does all that mean?

 When three or more ratios are equal, you can write an extended proportion.  A scale factor is a ratio of corresponding linear measurements of two similar figures.  So the scale factor of ABCD to GHIJ is.

 Are the triangles similar?  First identify pairs of congruent angles.  Now compare the ratios of corresponding sides. 12 C AB 8 16 F E D

A BC D E F G H Identify pairs of congruent angles. Compare the ratios of corresponding sides. Corresponding sides are not proportional, so the polygons are not similar Are the following polygons similar?

 CORN~PEAS C O R N P E A S 8 cm 9 cm 4 cm 72˚ Find the values of x and y. x y Example

Another example These pentagons are similar. Find the values for x, y, and z. 5 cm 4 cm 4.7 cm 7 cm 7.5 cm x y z

Time to practice…  In your textbook do the Lesson Check exercises 1-8 on page 444. These should be done in your notes.

Homework! Page 444 (9-20 all, all, 32, 34, 38)