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Transparency 5. Click the mouse button or press the Space Bar to display the answers. Splash Screen. Example 5-3c. Objective. Identify similar polygons and find missing measures of similar polygons. Example 5-3c. Vocabulary. Polygon.

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  1. Transparency 5 Click the mouse button or press the Space Bar to display the answers.

  2. Splash Screen

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

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

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

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

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

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

  9. Example 5-3c Math Symbols angle

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

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

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

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

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

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

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

  17. Example 5-2b Write a proportion using the 2 ratios Cross multiply 2 4 = Bring down = 3 x Bring down 2x = 2x 2x = 2x = 3(4) Multiply 3  4 2x = 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 2/3

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

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

  20. 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.B45 in.C84 in.D105 in. Example 5-3a The smaller What is the polygon has a perimeter of 42 inches perimeter of the larger polygon Big Polygon 2.5 Write a ratio (scale factor) of the similar polygons Small Polygon 1 Write a ratio of the perimeters of the similar polygons x Big Polygon 42 Small Polygon Define a variable of the unknown 3/3

  21. Example 5-3a Write a proportion of the 2 ratios x 2.5 Cross multiply = 42 1 Bring down = Bring down 1x = 1x = 2.5(42) 1x 1x = Multiply 2.5  42 1x = 1x = 105 x = 105 Use the Identify Property to multiply 1  x The variable is now by itself A 16.8 in.B45 in.C84 in.D105 in. Answer: D 3/3

  22. 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? A22 in.B34 in.C72 in.D269.5 in. Example 5-3c * Answer: A 3/3

  23. End of Lesson 5 Assignment

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