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Using Similarity

Using Similarity. Sarah Lewandowksi - Sterling Heights HS Andrew Esser - Sterling Heights HS. What is a GLCE?. What is a GLCE?. G rade L evel C ontent E xpectations. What does it mean?. G.TR.07.03 G=Geometry TR=Transformation and Symmetry 07=7 th Grade Expectation

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Using Similarity

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  1. Using Similarity Sarah Lewandowksi - Sterling Heights HS Andrew Esser - Sterling Heights HS

  2. What is a GLCE? What is a GLCE? Grade Level Content Expectations MMSTC

  3. What does it mean? G.TR.07.03 G=Geometry TR=Transformation and Symmetry 07=7th Grade Expectation 03=3rd Expectation MMSTC

  4. What does it mean? What does it mean? G.TR.07.06 G=Geometry TR=Transformation and Symmetry 07=7th Grade Expectation 06=6th Expectation MMSTC

  5. G.TR.07.03 G.TR.07.03 Understand that in similar polygons, corresponding angles are congruent and the ratios of corresponding sides are equal; understand the concepts of similar figures and scale factor. MMSTC

  6. G.TR.07.06 G.TR.07.06 Understand and use the fact that when two triangles are similar with scale factor of r, their areas are related by a factor of r². MMSTC

  7. Terminology What is a GLCE? Similarity- 1) Corresponding angles congruent 2) Length of corresponding sides proportional MMSTC

  8. Terminology What is a GLCE? Congruent- Equal Corresponding Angles or Sides- Same position in shape MMSTC

  9. Similar Triangles What is a GLCE? Scale Factor=3 MMSTC

  10. Correspondence What is a GLCE? Which angles are congruent? Which sides are proportional? A Scale Factor=2 B D C 24 E F MMSTC MMSTC

  11. Terminology What is a GLCE? Scale Factor- Divide or multiply shape by scale factor BC*1/2 = FG 6*1/2 = 3 Scale Factor=1/2 Or that the 1st quadrilateral Is 2x as big as the 2nd MMSTC

  12. Area What is a GLCE? AreaTriangle1 * r2 = AreaTriangle2 MMSTC

  13. Volume What is a GLCE? VolumeCube1 * r3 = VolumeCube2 MMSTC

  14. Volume What is a GLCE? V of cube 1 = 6 cm cubed Scale Factor = 3 V of cube 2 = 6 x 3 cubed = 6 x 27 = 162 Volume of Cube 2 is 162 cu cm v X r3 = V Volume = 6 Volume = 162 MMSTC

  15. Application What is a GLCE? Scale Factor- Architecture Designing Building MMSTC

  16. Application of Scale Factor What is a GLCE? MMSTC

  17. Recap What is a GLCE? Similarity- Corresponding angles are congruent Length of Corresponding Sides Proportional Scale Factor- Size of one shape in relation to another similar shape MMSTC

  18. Recap (cont’d) What is a GLCE? Areas of two similar triangles are related by a factor of scale factor squared Volumes in two similar 3 dimensional shapes are related by a factor of scale factor cubed MMSTC

  19. Resources What is a GLCE? http://media.wiley.com/Lux/89/18289.nfg002.jpg http://math8geometry.wikispaces.com/file/view/Similar1.png/33819751/Similar1.png http://www.dkhomedesign.com/dk-portfolio/houses/details.cfm?plan_no=20301 MMSTC

  20. Any Questions? MMSTC

  21. Quiz Time! MMSTC

  22. Question 1True or False?GLCE stands for Grade Level Content Expectations. MMSTC

  23. Question 2In similar polygons,_____ are congruent A. Corresponding Angles B. Corresponding Sides C. All angles D. Opposite angles MMSTC

  24. Question 3Which pair of polygons is similar? A. B. MMSTC

  25. Question 4 How much bigger is triangle 1 than triangle 2? MMSTC

  26. Question 5The Area of triangle 1 is 4. The scale factor to triangle 2 is 3. What is the area of triangle 2? A.12 C. 36 B.48 D. 6 MMSTC

  27. Question 6Which angles are congruent? A. B and G B. C and F C. D and E MMSTC

  28. Question 7What does the “TR” stand for in G.TR.07.06? A. Transformation and Scale Factor B. Trigonometry C. Triangle D. Transformation and Symmetry MMSTC

  29. Question 8 Name one of the ways scale factor is used in real life. MMSTC

  30. Question 9 Name a pair of corresponding angles (3) B + E C + F D + G MMSTC

  31. Correct! MMSTC

  32. Incorrect MMSTC

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