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11.7 Ratios of Areas

11.7 Ratios of Areas. Y. B. A. 10. 8. Z. X. 12. C. D. 9. Ratio of Areas:. What is the area ratio between ABCD and XYZ?. Steps: Set up fraction Write formulas Plug in numbers Solve and label with units. 1. Ratio A. A. 2. A = b 1 h 1. A = 1/2b 2 h 2.

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11.7 Ratios of Areas

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  1. 11.7 Ratios of Areas

  2. Y B A 10 8 Z X 12 C D 9 Ratio of Areas: What is the area ratio between ABCD and XYZ?

  3. Steps: Set up fraction Write formulas Plug in numbers Solve and label with units

  4. 1. Ratio A A 2. A = b1h1 A = 1/2b2h2 3. = 9•10 1/2 • 8 •12 = 90 48 =15 8

  5. D C A B Find the ratio of ABD to CBD When AB = 5 and BC = 2 Notice that the height of both triangles are congruent. When you set up the problem, the 1/2 and the height disappear leaving only 5/2 as the ratio.

  6. Similar triangles: Ratio corresponding of : altitudes medians angle bisectors equals the ratio of their corresponding sides.

  7. Q X 6 4 Y W P R Given ∆ PQR ∆WXY Find the ratio of the area. First find the ratio of the sides. QP = 6 XW 4 =3 2

  8. Q X 6 4 Y W P R A PQR = 1/2 b1h1 Ratio of area: AWXY 1/2 b2h2 = b1h1 b2h2 = 3•3 2 2 = 9 4

  9. Area ratio is the sides ratio squared! T109: If 2 figures are similar, then the ratio of their areas equals the square of the ratio of the corresponding segments. (similar-figures Theorem) A1 = S12 When A1 and A2 are areas and S1 and S2 are measures of corresponding segments. A2 S2

  10. A C M B Corresponding Segments include: Sides, altitudes, medians, diagonals, and radii. Ex. AM is the median of ∆ABC. Find the ratio of A ∆ ABM : A ∆ACM Notice these are not similar figures!

  11. A C M B 1. Altitude from A is congruent for both triangles. Label it X. BM = MC because AM is a median. Let y = BM and MC. A∆ABM = 1/2 b1h1 A ∆ACM 1/2 b2h2 = 1/2 xy 1/2 xy = 1 Therefore the ratio is 1:1 They are equal !

  12. T110: The median of a triangle divides the triangle into two triangles with equal area.

  13. Find the ratios: 9cm 9cm 10cm 10cm

  14. Find the ratio 2 6

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