Warm-Up Exercises Groups will read pages Group One will explain Example One on page 367 and will explain problem 22 on page 372 Group Two will explain the Key concept on the bottom of page 367 and example 2 Group Three will explain the two guided practice questions on page 368 Group Four will explain example 3 on the bottom of page 368 Group Five will explain example 4 on page 369 Group Six will explain the guided practice on the bottom of page 369

Warm-Up Exercises EXAMPLE 1 Describe a dilation FEG is similar to FDH. Describe the dilation that moves FEG onto FDH. SOLUTION The figure shows a dilation with center F. The scale factor is 2 because the ratio of FH to FG is 20 : 10, or 2 : 1.

Warm-Up Exercises EXAMPLE 2 Describe a combination of transformations ABC is similar to FGE. Describe a combination of transformations that moves ABC onto FGE. SOLUTION A dilation with center B and scale factor moves ABC onto DBE. Then a rotation of DBE with center E moves DBE onto FGE. The angle of rotation is equal to the measure of C. 2 3

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2 The two figures are similar. Describe the transformation(s) that move the blue figure onto the red figure. 1. dilation with center B and scale factor ANSWER ANSWER dilation with scale factor and reflection 2 3

Warm-Up Exercises EXAMPLE 3 Use transformations to show figures are not similar Use transformations to explain why ABCDE and KLQRP are not similar.

Warm-Up Exercises EXAMPLE 3 Use transformations to show figures are not similar SOLUTION Corresponding sides in the pentagons are proportional with a scale factor of. 2 3 However, this does not necessarily mean the pentagons are similar. A dilation with center A and scale factor moves ABCDE onto AFGHJ. Then a reflection moves AFGHJ onto KLMNP. 2 3 KLMNP does not exactly coincide with KLQRP, because not all of the corresponding angles are congruent. (Only A and K are congruent.) Since angle measure is not preserved, the two pentagons are not similar.

Warm-Up Exercises EXAMPLE 4 Use similar figures 1 2 GRAPHIC DESIGN A design for a party mask is made using all equilateral triangles and a scale factor of. a. Describe transformations that move triangle A onto triangle B. Describe why triangles C and D are similar by using the given information. b.

Warm-Up Exercises EXAMPLE 4 Use similar figures a.The figure shows a dilation with scale factor followed by a clockwise rotation of 60°. Triangles C and D are similar because all pairs of corresponding sides are proportional with a ratio of and all pairs of corresponding angles of equilateral triangles have the same measure. b. SOLUTION

Warm-Up Exercises GUIDED PRACTICE for Examples 3 and 4 Refer to the floor tile designs shown below. In each design, the red shape is a regular hexagon.

Warm-Up Exercises GUIDED PRACTICE for Examples 3 and Tile design 1 is made using two hexagons. Explain why the red and blue hexagons are not similar. Tile design 2 is made using two similar geometric shapes. Describe the transformations that move the blue hexagon to the red hexagon. 6. Tile design 3 shows congruent angles and sides. Explain why the red and blue hexagons are similar, using the given information. If the lengths of all the sides of one polygon are proportional to the lengths of all the corresponding sides of another polygon, must the polygons be similar? Explain.

Warm-Up Exercises GUIDED PRACTICE for Examples 3 and The red hexagon has all sides congruent, but the blue hexagon has 3 shorter sides and 3 longer sides, so ratios of corresponding side lengths are not constant. dilation followed by a rotation of 30° about the center of the figures 6. All angles are congruent, so angle measure is preserved, and all side lengths are congruent in each hexagon, so the ratio of any two corresponding side lengths is constant. No; even though corresponding sides might be proportional, if corresponding angles are not congruent, the polygons are not similar. SAMPLE ANSWER

Warm-Up Exercises

An artist wants to paint a picture. She wants the canvas to be a golden rectangle with its longer horizontal sides 31 cm wide. To the nearest 100 th of a cm, how wide should the canvas be?

Warm-Up Exercises The sides of a pentagon are 7,15, 9, 18, and 12. The longest side of a similar pentagon is 40. What is the perimeter of the similar pentagon?

Warm-Up Exercises Are the triangles similar? If so, write the similarity ratio, the similarity statement, and name the postulate or theorem that you can use to prove they are similar. Also, explain how you can use the postulate or theorem. If not, write not similar and explain why they are not similar.

Warm-Up Exercises The Sears Tower in Chicago is 1444 feet high. A model of the tower is 48 INCHES tall. What is the ratio of the height of the model to the height of the actual Sears Tower?