Five-Minute Check (over Lesson 7–1) Mathematical Practices Then/Now New Vocabulary Example 1: Determine Whether Polygons Are Similar Key Concept: Similar Polygons Example 2: Use a Similarity Statement Example 3: Real-World Example: Identify Similar Polygons Example 4: Use Similar Figures to Find Missing Measures Key Concept: Properties of Similarity Theorem 7.1: Perimeters of Similar Polygons Example 5: Use a Scale Factor to Find Perimeter Lesson Menu

There are 480 sophomores and 520 juniors in a high school There are 480 sophomores and 520 juniors in a high school. Find the ratio of juniors to sophomores. A. 10:8 B. 13:12 C. 19:17 D. 22:20 5-Minute Check 1

A strip of wood molding that is 33 inches long is cut into two pieces whose lengths are in the ratio of 7:4. What are the lengths of the two pieces? A. 7 in., 4 in. B. 14 in., 8 in. C. 18 in., 15 in. D. 21 in., 12 in. 5-Minute Check 2

A. 7 B. 8 C. 9 D. 10 5-Minute Check 3

A. 2.75 B. 3.25 C. 3.75 D. 4.25 5-Minute Check 4

A. 4 B. 3 C. 2 D. 1 5-Minute Check 5

The standard ratio of a photo’s width to its length is The standard ratio of a photo’s width to its length is . What is the length of a photo that has a width of 14 inches? A. 9.3 inches B. 17 inches C. 20 inches D. 56 inches 5-Minute Check 6

Mathematical Practices 1 Make sense of problems and persevere in solving them. 6 Attend to precision. Content Standards G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. G. SRT. 3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. MP

You drew the image of a figure after a dilation. Use the definition of similarity to identify similar polygons. Solve problems by using the properties of similar polygons. Then/Now

similar polygons similarity transformation scale factor New Vocabulary

Determine whether the given polygons are similar. Explain. Determine Whether Polygons Are Similar Determine whether the given polygons are similar. Explain. A. ABCD and EFGH Example 1A

Are the polygons the same shape? Yes Determine Whether Polygons Are Similar Are the polygons the same shape? Yes Will a transformation map one polygon to the other? Yes Is one polygon a scale of the other? Yes Yes Are the polygons similar? Answer: Yes; map ABCD to EFGH using a dilation centered at the origin with scale factor followed by a translation along [– 2, 4]. Example 1A

Determine whether the given polygons are similar. Explain. Determine Whether Polygons Are Similar Determine whether the given polygons are similar. Explain. B. PQR and STU Example 1B

Are the triangles the same shape? No Determine Whether Polygons Are Similar Are the triangles the same shape? No Will a transformation map one triangle to the other? No Are the triangles similar? No Answer: No; the triangles do not have the same shape, so there are no similarity transformations that will map one to the other. Example 1B

Key Concept

List the congruent angle pairs. Use a Similarity Statement If ABC ∼ RST, list all pairs of congruent angles and write a proportion that relates the corresponding sides. List the congruent angle pairs. A ≅ R, B ≅ S, C ≅ T Example 2

List the corresponding similar sides. Use a Similarity Statement List the corresponding similar sides. AB ~ RS, BC ~ ST, AC ~ RT Write a proportion that relates to the corresponding sides. Answer: Example 2

Menus Tan is designing a new menu for the Identify Similar Polygons Menus Tan is designing a new menu for the restaurant where he works. Determine whether the following sizes for the new menu are similar to the original menu. If so, write the similarity statement and scale factor. Explain your reasoning. Real-World Example 3

Write a proportion that relates to the corresponding sides. Identify Similar Polygons A. Write a proportion that relates to the corresponding sides. Real-World Example 3A

Substitute the lengths of the sides. Identify Similar Polygons Substitute the lengths of the sides. Simplify. Are the fractions equal? No The menus are not similar because the sides are not proportional. Answer: Real-World Example 3A

Write a proportion that relates to the corresponding sides. Identify Similar Polygons B. Write a proportion that relates to the corresponding sides. Real-World Example 3B

Substitute the lengths of the sides. Identify Similar Polygons Substitute the lengths of the sides. Simplify. Are the fractions equal? Yes The menus are similar because the sides are proportional. Answer: Real-World Example 3B

The two polygons are similar. Use Similar Figures to Find Missing Measures The two polygons are similar. A. Find x. Example 4A

Write a proportion that relates to the corresponding sides. Use Similar Figures to Find Missing Measures Write a proportion that relates to the corresponding sides. Substitute the lengths of the sides. Solve for x. Answer: Example 4A

The two polygons are similar. Use Similar Figures to Find Missing Measures The two polygons are similar. B. Find y. Example 4B

Answer: Write a proportion that relates to the corresponding sides. Use Similar Figures to Find Missing Measures Write a proportion that relates to the corresponding sides. Substitute the lengths of the sides. Solve for y Answer: Example 4B

Key Concept

Theorem

Use a Scale Factor to Find Perimeter If ABCDE ∼ RSTUV, find the scale factor of from RSTUV to ABCDE and the perimeter of each polygon. Example 5

List the corresponding similar sides. Use a Scale Factor to Find Perimeter List the corresponding similar sides. AB ~ RS, BC ~ ST, CD ~ TU, DE ~ UV, AE ~ VR Write a proportion that relates to the corresponding sides. Find the lengths of the missing side ST. Example 5

Find the lengths of the missing side DC. Use a Scale Factor to Find Perimeter Solve for y. Find the lengths of the missing side DC. Solve for x. Example 5

Find the perimeter of each polygon: Use a Scale Factor to Find Perimeter Find the perimeter of each polygon: ABCDE = 4 + 4 + 6 + 6 + 6 = 26 RSTUV = 7 + 7 + 10.5 + 10.5 + 10.5 = 45.5 Answer: scale factor: perimeter of ABCDE: 26; perimeter of RSTUV: 45.5 Example 5