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D. N. A. 1) Find the ratio of BC to DG. 2) Solve each proportion.

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Presentation on theme: "D. N. A. 1) Find the ratio of BC to DG. 2) Solve each proportion."— Presentation transcript:

1 D. N. A. 1) Find the ratio of BC to DG. 2) Solve each proportion.

2 SlidesSkills PracticePractice 1, 4, 51-2 17, 21-273-6

3 Similar Polygons Chapter 7-2

4 Lesson 2 MI/Vocab similar polygons scale factor Identify similar figures. Solve problems involving scale factors. Standard 11.0 Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids.

5 Similar Polygons Have congruent corresponding angles. Have proportional corresponding sides. “~” means “is similar to” A B D C F G H E ABCD ~ EFGH  A   E  B   F  C   G  D   H

6 Writing Similarity Statements Decide if the polygons are similar. If they are, write a similarity statement. A B C D 6 12 9 15 W X Z Y 10 8 6 4  A   W  B   Y  C   Z  D   X All corr. sides are proportionate and all corr. angles are  ABCD ~ WYZX

7 Scale Factor The ratio of the lengths of two corresponding sides. In the previous example the scale factor is 3:2.

8 Lesson 2 Ex1 Similar Polygons A. Determine whether each pair of figures is similar. Justify your answer. The vertex angles are marked as 40º and 50º, so they are not congruent.

9 Lesson 2 Ex1 Similar Polygons Answer: None of the corresponding angles are congruent, so the triangles are not similar. Since both triangles are isosceles, the base angles in each triangle are congruent. In the first triangle, the base angles measure and in the second triangle, the base angles measure

10 Lesson 2 Ex1 Similar Polygons B. Determine whether each pair of figures is similar. Justify your answer. All the corresponding angles are congruent.

11 Lesson 2 Ex1 Similar Polygons Now determine whether corresponding sides are proportional. The ratios of the measures of the corresponding sides are equal. Answer: The ratio of the measures of the corresponding sides are equal and the corresponding angles are congruent, so ΔABC ~ ΔRST.

12 Lesson 2 CYP1 A.Yes, ΔAXE ~ ΔWRT. B.Yes, ΔAXE ~ ΔRWT. C.No, the Δ's are not ~. D.not enough information A. Determine whether the pair of figures is similar.

13 Lesson 2 CYP1 A.Yes, ΔTRS ~ ΔNGA. B.Yes, ΔTRS ~ ΔGNA. C.No, the Δ's are not ~. D.not enough information B. Determine whether the pair of figures is similar.

14 Lesson 2 Ex2 ARCHITECTURE An architect prepared a 12-inch model of a skyscraper to look like a real 1100-foot building. What is the scale factor of the model compared to the real building? Before finding the scale factor you must make sure that both measurements use the same unit of measure. 1 foot = 12 inches

15 Lesson 2 Ex2 Answer: The ratio comparing the two heights is or 1:1100. The scale factor is, which means that the model is the height of the real skyscraper. Animation: Similar Polygons

16 Each pair of polygons is similar. Find x and y. 1) 2) 3)

17 Lesson 2 CYP2 A space shuttle is about 122 feet in length. The Science Club plans to make a model of the space shuttle with a length of 24 inches. What is the scale factor of the model compared to the real space shuttle? A. B. C. D.

18 Lesson 2 Ex3 Proportional Parts and Scale Factor A. The two polygons are similar. Write a similarity statement. Then find x, y, and UV. Use the congruent angles to write the corresponding vertices in order. polygon ABCDE ~ polygon RSTUV

19 Lesson 2 Ex3 Proportional Parts and Scale Factor Now write proportions to find x and y. To find x: Similarity proportion Cross products Multiply. Divide each side by 4.

20 Lesson 2 Ex3 Proportional Parts and Scale Factor To find y: Similarity proportion Cross products Multiply. Subtract 6 from each side. Divide each side by 6 and simplify. AB = 6, RS = 4, DE = 8, UV = y + 1

21 Lesson 2 Ex3 Proportional Parts and Scale Factor

22 Lesson 2 Ex3 Proportional Parts and Scale Factor B. The two polygons are similar. Find the scale factor of polygon ABCDE to polygon RSTUV. The scale factor is the ratio of the lengths of any two corresponding sides. Answer:

23 Lesson 2 CYP3 A.TRAP ~ OZDL B.TRAP ~ OLDZ C.TRAP ~ ZDLO D.TRAP ~ ZOLD A. The two polygons are similar. Write a similarity statement.

24 Lesson 2 CYP3 A.a = 1.4 B.a = 3.75 C.a = 2.4 D.a = 2 B. The two polygons are similar. Solve for a.

25 Lesson 2 CYP3 C. The two polygons are similar. Solve for b. A.b = 7.2 B.b = 1.2 C. D.b = 7.2

26 Lesson 2 CYP3 D. The two polygons are similar. Solve for ZO. A.7.2 B.1.2 C.2.4 D.

27 1.A 2.B 3.C 4.D Lesson 2 CYP3 E. The two polygons are similar. What is the scale factor of polygon TRAP to polygon ZOLD? A. B. C. D.

28 Lesson 2 Ex4 Rectangle WXYZ is similar to rectangle PQRS with a scale factor of 1.5. If the length and width of PQRS are 10 meters and 4 meters, respectively, what are the length and width of rectangle WXYZ? Enlargement or Reduction of a Figure Write proportions for finding side measures. Let one long side of each WXYZ and PQRS be and one short side of each WXYZ and PQRS be

29 Lesson 2 Ex4 Enlargement or Reduction of a Figure WXYZ PQRS

30 Lesson 2 CYP4 A.9.8 in, 19.6 in B.7 in, 14 in C.6 in, 12 in D.5 in, 10 in Quadrilateral GCDE is similar to quadrilateral JKLM with a scale factor of. If two of the sides of GCDE measure 7 inches and 14 inches, what are the lengths of the corresponding sides of JKLM?

31 Lesson 2 Ex5 Scales on Maps The scale on the map of a city is inch equals 2 miles. On the map, the width of the city at its widest point is inches. The city hosts a bicycle race across town at its widest point. Tashawna bikes at 10 miles per hour. How long will it take her to complete the race? Explore Every equals 2 miles. The distance across the city at its widest point is

32 Lesson 2 Ex5 Scales on Maps Solve Cross products The distance across the city is 30 miles. Plan Create a proportion relating the measurements to the scale to find the distance in miles. Then use the formula to find the time. Divide each side by 0.25.

33 Lesson 2 Ex5 Answer: 3 hours Scales on Maps Divide each side by 10. It would take Tashawna 3 hours to bike across town. Examine To determine whether the answer is reasonable, reexamine the scale. If 0.25 inches = 2 miles, then 4 inches = 32 miles. The distance across the city is approximately 32 miles. At 10 miles per hour, the ride would take about 3 hours. The answer is reasonable.

34 Lesson 2 CYP5 A.3.75 hr B.1.25 hr C.5 hr D.2.5 hr An historic train ride is planned between two landmarks on the Lewis and Clark Trail. The scale on a map that includes the two landmarks is 3 centimeters = 125 miles. The distance between the two landmarks on the map is 1.5 centimeters. If the train travels at an average rate of 50 miles per hour, how long will the trip between the landmarks take?

35 Forced Perspective

36 Using Ratios Example #1 The Perimeter of a rectangle is 60 cm. The ratio of AB:BC is 3:2. Find the length and width of the rectangle. A D C B 3:2 is in lowest terms. AB:BC could be 3:2, 6:4, 9:6, 12:8, etc. AB = 3x BC = 2x Perimeter = l + w+ l + w 60 = 3x + 2x + 3x + 2x 60 = 10x x = 6 L = 3(6) = 18 W = 2(6) = 12

37 Find the measures of the sides of each triangle. 12. The ratio of the measures of the sides of a triangle is 3:5:7, and its perimeter is 450 centimeters. 13. The ratio of the measures of the sides of a triangle is 5:6:9, and its perimeter is 220 meters. 14. The ratio of the measures of the sides of a triangle is 4:6:8, and its perimeter is 126 feet. Find the measures of the angles in each triangle. 15) The ratio of the measures of the angles is 4:5:6.

38 m  A+ m  B+ m  C = 180 o Triangle Sum Thm. 2x + 3x + 4x = 180 o 9x = 180 o x = 20 o m  A = 40 o m  B = 60 o m  C = 80 o The angle measures in  ABC are in the extended ratio of 2:3:4. Find the measure of the three angles. Using Ratios Example #2 A C B 2x 3x 4x

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