1. Geometry 8.3 Similar Polygons

2. July 2, 2015Geometry 8.3 Similar Polygons2 Goals Identify similar polygons Find the ratio of similarity between similar figures. Solve problems involving similar figures.

3. July 2, 2015Geometry 8.3 Similar Polygons3 Similar Polygons ABCD and RSTV are similar polygons: Corresponding angles are congruent. Corresponding sides are proportional. R S T V 10 8 6 A B C D 15 12 9 9 6

4. July 2, 2015Geometry 8.3 Similar Polygons4 Similar Polygons Corresponding angles are congruent:  A   R,  B   S,  C   T,  D   V R S T V 10 8 6 A B C D 15 12 9 9 6

5. July 2, 2015Geometry 8.3 Similar Polygons5 Similar Polygons Corresponding sides are proportional: R S T V 10 8 6 A B C D 15 12 9 9 6

6. July 2, 2015Geometry 8.3 Similar Polygons6 Similar Polygons Corr.  s  Sides prop. ABCD ~ RSTV R S T V 10 8 6 A B C D 15 12 9 9 6

7. July 2, 2015Geometry 8.3 Similar Polygons7 Similar Polygons Corresponding Angles are congruent. Corresponding Sides are proportional. Use the symbol “~” for similar. To show that two polygons are similar, you must prove both things: angles congruent, sides proportional.

8. July 2, 2015Geometry 8.3 Similar Polygons8 Similarity Statements List the congruent angles. Write the ratios of the corresponding sides. 70  J K L Q R S  J   Q,  K   S,  L   R

9. July 2, 2015Geometry 8.3 Similar Polygons9 Example Are these figures similar? Yes Why? Corr. angles congruent Corr. sides proportional. E N F G H M O P 3 2 4 1.5 6 8 34

10. July 2, 2015Geometry 8.3 Similar Polygons10 Write the similarity statements. E N F G H M O P EFGH ~ NMPO Or: HEFG ~ ONMP, GFEH ~ PMNO, EHGF ~ NOPM, etc. 3 2 4 1.5 6 8 34

11. July 2, 2015Geometry 8.3 Similar Polygons11 Scale Factor If two polygons are similar, the ratio of two corresponding sides is called the scale factor.

12. July 2, 2015Geometry 8.3 Similar Polygons12 Scale Factor The scale factor of  JKL to  QSR is 10/5 or 2/1. The scale factor of  QSR to  JKL is 5/10 or 1/2. 70  J K L Q R S 10 5

13. July 2, 2015Geometry 8.3 Similar Polygons13 Perimeter and Similar Figures AB CD FG HI 10 4 14 5 z yx 1.ABCD ~ FGHI 2.Find the scale factor of ABCD to FGHI. 3.Find the values of x, y, and z. 4.Find the perimeter of ABCD and FGHI. 5.Find the ratio of the perimeters.

14. July 2, 2015Geometry 8.3 Similar Polygons14 Perimeter and Similar Figures AB CD FG HI 10 4 14 5 z yx 2. Find the scale factor from ABCD to FGHI. The only known corresponding sides are AB and FG.

15. July 2, 2015Geometry 8.3 Similar Polygons15 Perimeter and Similar Figures AB CD FG HI 10 4 14 5 z yx 3. Find the values of x, y, and z.

16. July 2, 2015Geometry 8.3 Similar Polygons16 Perimeter and Similar Figures AB CD FG HI 10 4 14 5 2 77 4. Find the perimeter of ABCD and FGHI. P = 42 P = 21

17. July 2, 2015Geometry 8.3 Similar Polygons17 Perimeter and Similar Figures AB CD FG HI 10 4 14 5 2 77 5. Find the ratio of the perimeters. P = 42 P = 21 Ratio of perimeters2:1 Ratio of Similarity2:1

18. July 2, 2015Geometry 8.3 Similar Polygons18 Theorem 8.1 If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths and is equal to the similarity ratio.

19. July 2, 2015Geometry 8.3 Similar Polygons19 Theorem 8.1 Example 20 8 P = 100 P = ? These figures are similar. Find the perimeter of the smaller one.

20. July 2, 2015Geometry 8.3 Similar Polygons20 Problems to Solve

21. July 2, 2015Geometry 8.3 Similar Polygons21 Problem 1 20 4 8 6 y – 2 x + 6 Solve for x and y if the triangles are similar.

22. July 2, 2015Geometry 8.3 Similar Polygons22 Problem 1 Solution 20 4 8 6 y – 2 x + 6 Scale Factor is 20/8 Solve for x Solve for y

23. July 2, 2015Geometry 8.3 Similar Polygons23 Problem 2 60 x + 10 95  85  100  yy 24 32 Find x and y if the figures are similar.

24. July 2, 2015Geometry 8.3 Similar Polygons24 Problem 2 Solution 60 x + 10 95  85  100  yy 24 32 Similarity Ratio y = 360  - 100  - 85  - 95  y = 80 

25. July 2, 2015Geometry 8.3 Similar Polygons25 Problem 3  ABC ~  RST AB = 20 ST = 4 BC = RS Find BC and RS.

26. July 2, 2015Geometry 8.3 Similar Polygons26 Problem 3 Solution  ABC ~  RST AB = 20 ST = 4 BC = RS Find BC and RS. A BC R ST 20 4 x x

27. July 2, 2015Geometry 8.3 Similar Polygons27 Problem 3 Solution A BC R ST 20 4 x x  ABC ~  RST

28. July 2, 2015Geometry 8.3 Similar Polygons28 Problem 4 You want to print a picture in your camera. You have two sizes of paper for your printer: 4 × 6 and 5 × 7. Does it matter? Will the pictures printed from each size of paper be similar? 4 × 6 5 × 7 Sides not proportional, figures not similar.

29. July 2, 2015Geometry 8.3 Similar Polygons29 Problem 5 MNOP has a perimeter of 24. Find the perimeter of QRST if MN = 8 and QR = 12.

30. July 2, 2015Geometry 8.3 Similar Polygons30 Summary Two polygons are similar if they have the same shape, but a different size. If polygons are similar corresponding angles are congruent, and corresponding sides are proportional. The ratio of any two corresponding sides is the scale factor. The ratio of the perimeters is equal to the ratio of two corresponding sides.