Unit 8.3 Similar Polygons

Warm-up Find the measure of the angles in the figure below V 61 U W 56 X

Similar Polygons in real life Write down five things that you notice about this artwork by M.C. Escher?

Section 8.3 Similar Polygons What do you notice about the sides of the above triangles?

What is Similarity? Similar Triangles Not Similar Similar Similar Pass out the following materials for each student: one sheet of blank paper (8.5 in. X 11 in.) protractor ruler Instruct the students to fold their paper like this: Questions:       Describe the polygons that were created.       Do you know any of the angle measurements or linear measurements by observation? Explain. Instruct the students to label the points of the triangles: Questions:       Name the polygons using the labeling letters.       Name the angle and/or linear measurements using the labeling letters. Similar Not Similar

Section 8.3 Similar Polygons Correspondence between two polygons Corresponding angles are congruent Lengths of the sides of the polygon are proportional The is used to show similarity List all of the pairs of the congruent angles.

Comparing Photographic Enlargements 5 x 3.5 16 You have been asked to create a poster to advertise a new CD for Chris Brown You have a 3.5 inch by 5 inch photo for you to enlarge. You want the enlargement to be 16 inches wide. How long will it be?

What is the scale factor? What is a scale factor If two polynomials are similar, then the ratio of the lengths of two corresponding sides is called the scale factor. Q 6 R X 4 Y 10 15 W B P S What is the scale factor? Draw Example on the board

Analysis of two similar triangles: Statement of proportionality is called the scale factor (also ratio of similitude)   AA To show triangles are similar, it is sufficient to show that two angles of one triangle are congruent (equal) to two angles of the other triangle.

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

Independent Task Use the dot paper to create the following Two similar right triangles Two similar rectangles Two similar scalene triangles Answer the following questions. How do you know your figures are similar? What are the scale factors between your figures? Write similarity statements for each of your figures. Find the perimeters for your right triangles and rectangles. What do you notice when compared to the scale factor?