Similarity day 1 with activity

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Similarity day 1 with activity

  1. 1. GT Geom Drill 3.17 1. Take out HW and a pen and put it on the corner of your desk. 2. Objective: STW write and simplify ratios and use proportions to solve problems. STW discover properties of similar polygons
  2. 2. GT Geometry Drill #3.17 2/28/14 Solve for X 1. x 3 2 3. 4 3 2 8 5 x 4. 1 2 4x 2. 2x 1 3 x 1 x 2 10 3x 2
  3. 3. GT Geometry Drill #3.17 2/28/14 5. The ratio of the side lengths of a triangle is 4:7:5, and its perimeter is 96 cm. What is the length of the shortest side? Let the side lengths be 4x, 7x, and 5x. Then 4x + 7x + 5x = 96 . After like terms are combined, 16x = 96. So x = 6. The length of the shortest side is 4x = 4(6) = 24 cm. 6. The ratio of the angle measures in a triangle is 1:6:13. What is the measure of each angle?
  4. 4. 7-1 Ratio and Proportion The ratio of the angle measures in a triangle is 1:6:13. What is the measure of each angle? x + y + z = 180° x + 6x + 13x = 180° 20x = 180° x = 9° y = 6x z = 13x y = 6(9°) z = 13(9°) y = 54° z = 117° Holt McDougal Geometry
  5. 5. 7-1 Ratio and Proportion ? Holt McDougal Geometry ? ?
  6. 6. 7-1 Ratio and Proportion 21 6 8 2 8 4 27 20 10 Holt McDougal Geometry 24 8 16 20 12 3 28 15 3 15 15 36 5 12 14
  7. 7. 7-1 Ratio and Proportion Example 4: Using Properties of Proportions Given that 18c = 24d, find the ratio of d to c in simplest form. 18c = 24d Divide both sides by 24c. Simplify. Holt McDougal Geometry
  8. 8. 7-1 Ratio and Proportion Check It Out! Example 4 Given that 16s = 20t, find the ratio t:s in simplest form. 16s = 20t Divide both sides by 20s. Simplify. Holt McDougal Geometry
  9. 9. 7-1 Ratio and Proportion Example 5: Problem-Solving Application Marta is making a scale drawing of her bedroom. Her rectangular room is 12 feet wide and 15 feet long. On the scale drawing, the width of her room is 5 inches. What is the length? 1 Understand the Problem The answer will be the length of the room on the scale drawing. Holt McDougal Geometry
  10. 10. 7-1 Ratio and Proportion Example 5 Continued 2 Make a Plan Let x be the length of the room on the scale drawing. Write a proportion that compares the ratios of the width to the length. Holt McDougal Geometry
  11. 11. 7-1 Ratio and Proportion Example 5 Continued 3 Solve 5(15) = x(12.5) Cross Products Property 75 = 12.5x x=6 Simplify. Divide both sides by 12.5. The length of the room on the scale drawing is 6 inches. Holt McDougal Geometry
  12. 12. Agree or Disagree 1. If two figures are similar then they are congruent 2. If the ratios of the length of corresponding sides of two triangles are equal, then the triangles are congruent. 3. If triangles are similar then they have the same shape 4. If two triangles are congruent then each pair of corresponding angles are congruent. 5. If two angles of one triangle are congruent to corresponding angles of another triangle, then the triangles are similar
  13. 13. Vocabulary similar similar polygons similarity ratio
  14. 14. Figures that are similar (~) have the same shape but not necessarily the same size.
  15. 15. Two polygons are similar polygons if and only if their corresponding angles are congruent and their corresponding side lengths are proportional.
  16. 16. Proving Similar Triangles • Are the triangles similar? 15 12 20 16 18 24
  17. 17. Are these similar? 1 5 18 2 6
  18. 18. Scale Factor The ratio of the lengths of two corresponding sides of similar polygons.

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