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4. Example 5-3c Objective Identify similar polygons and find missing measures of similar polygons

5. Example 5-3c Vocabulary Polygon A simple closed figure in a plane formed by three or more line segments

6. Example 5-3c Vocabulary Similar Polygons that have the same shape  Is similar to

7. Example 5-3c Vocabulary Corresponding parts Parts of a similar figure that “match”

8. Example 5-3c Vocabulary Congruent Parts of a geometric figure that have the same measure  is congruent to

9. Example 5-3c Vocabulary Scale factor A ratio of the lengths of two corresponding sides of two similar polygons

10. Example 5-3c Math Symbols angle

11. Example 5-3c Math Symbols Segment AB AB Measure of AB AB

12. Lesson 5 Contents Example 1Identify Similar Polygons Example 2Find Missing Measures Example 3Scale Factor and Perimeter

13. Example 5-1a Determine whether triangle DEF is similar to triangle HJK. Explain your reasoning. First, check to see if corresponding angles are congruent. and 1/3

14. Example 5-1a Next, check to see if corresponding sides are proportional. 1/3 Change ratio to decimal Compare the decimals Answer: Angles are equal and ratios of sides are equal so triangles are similar

15. Example 5-1c Determine whether triangle ABC is similar to triangle TRI. Explain your reasoning. Answer: Yes; corresponding angles are congruent and A C B T IR 1/3

16. Example 5-2a Given that rectangle GHIJ ~ rectangle LMNO, write a proportion to find the measure of Then solve. 2/3 Write a proportion of the rectangles from known similar sides Small rectangle Large rectangle 2 3 Define a variable for measure of NO x

17. Example 5-2a 2/3 Write a proportion of the rectangles from a known similar sides with the unknown “n” Small rectangle 4 nLarge rectangle x

18. Example 5-2b Write a proportion using the 2 ratios 2/3 2 3 4 = x Cross multiply 2x Bring down = 2x =2x = 3(4) Bring down 2x = 2x = Multiply 3  4 2x = 12 Ask “what is being done to the variable?” The variable is being multiplied by 2 Do the inverse on both sides of the = sign

19. Example 5-2b Answer: Measure of NO = 6 2/3 2 3 4 = x 2x 2x =2x = 3(4) 2x =2x = 12 Do the inverse on both sides of the = sign Bring down 2x = 12 2x = 12 Using the fraction bar, divide both sides by 2 2 2 Combine “like” terms 1  x Bring down = 1  x = Combine “like” terms 1  x = 6 Use the Identify Property to multiply 1  x x Bring down = 6 x = 6 Find the measure of

20. Example 5-2c Given that rectangle ABCD ~ rectangle WXYZ, write a proportion to find the measure of Then solve. Answer: = 15 2/3

21. Example 5-3a MULTIPLE- CHOICE TEST ITEM A polygon has sides 2.5 times as long as a similar polygon. The smaller polygon has a perimeter of 42 inches. What is the perimeter of the larger polygon? A 16.8 in. B 45 in. C 84 in. D 105 in. 3/3 Write a ratio (scale factor) of the similar polygons Big Polygon Small Polygon 2.5 1 Write a ratio of the perimeters of the similar polygons Big Polygon What is the perimeter of the larger polygon Define a variable of the unknown x Small Polygon The smaller polygon has a perimeter of 42 inches 42

22. Example 5-3a 3/3 2.5 1 x 42 Write a proportion of the 2 ratios = Cross multiply 1x Bring down = 1x =1x = 2.5(42) Bring down 1x = 1x = Multiply 2.5  42 1x = 105 Use the Identify Property to multiply 1  x x = 105 The variable is now by itself A 16.8 in. B 45 in. C 84 in. D 105 in. Answer: D

23. Example 5-3c MULTIPLE- CHOICE TEST ITEM A polygon has sides 3.5 times as long as a similar polygon. The larger polygon has a perimeter of 77 inches. What is the perimeter of the smaller polygon? A 22 in. B 34 in. C 72 in. D 269.5 in. Answer: A * 3/3

24. End of Lesson 5 Assignment Lesson 4:5Similar Polygons3 - 14 All