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8.4A Similar Triangles and Slope

8.4A Similar Triangles and Slope. Identify similar triangles. Use similar triangles to help in developing an understanding of slope, m, given as a rate comparing the change in y-values and x-values. Objectives/Assignment. Identifying Similar Triangles.

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8.4A Similar Triangles and Slope

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  1. 8.4A Similar Triangles and Slope

  2. Identify similar triangles. Use similar triangles to help in developing an understanding of slope, m, given as a rate comparing the change in y-values and x-values. Objectives/Assignment

  3. Identifying Similar Triangles • In this lesson, you will continue the study of similar polygons by looking at the properties of similar triangles. • In this lesson, you will use similar triangles and polygons to develop an understanding of slope

  4. In the diagram, ∆BTW ~ ∆ETC. Write the statement of proportionality. Find mTEC. Find ET and BE. Ex. 1: Writing Proportionality Statements 34° 79° *****Pay close attention to where each segment is located.

  5. In the diagram, ∆BTW ~ ∆ETC. Write the statement of proportionality. Ex. 1: Writing Proportionality Statements 34° ET TC CE = = BT TW WB 79° *****Pay close attention to how this ratio is set up. Look at where the segments are located.

  6. In the diagram, ∆BTW ~ ∆ETC. Find mTEC. B  TEC, SO mTEC = 79° Ex. 1: Writing Proportionality Statements 34° 79°

  7. In the diagram, ∆BTW ~ ∆ETC. Find ET and BE. Ex. 1: Writing Proportionality Statements 34° CE ET Write proportion. = WB BT 3 ET Substitute values. = 12 20 3(20) ET Multiply each side by 20. = 79° 12 5 = ET Simplify. Because BE = BT – ET, BE = 20 – 5 = 15. So, ET is 5 units and BE is 15 units.

  8. If two angles of one triangle are congruent to the two angles of another triangle, then the two triangles are similar. If JKL  XYZ and KJL  YXZ, then ∆JKL ~ ∆XYZ. Angle-Angle Similarity Postulate

  9. ∆ ADF ~ ∆ BCE Use the properties of similar triangles to explain why any two points on a line can be used to calculate slope. Find the slope of the line using both pairs of points shown. Ex. 3: Why a Line Has Only One Slope

  10. By the AA Similarity Postulate, ∆BEC ~ ∆AFD, so the ratios of corresponding sides are the same. In particular, Ex. 3: Why a Line Has Only One Slope CE BE By a property of proportions, = DF AF CE DF = BE AF

  11. The slope of a line is the ratio of the change in y to the corresponding change in x. The ratios Ex. 3: Why a Line Has Only One Slope Represent the slopes of BC and AD, respectively. and CE BE DF AF

  12. Because the two slopes are equal, any two points on a line can be used to calculate its slope. You can verify this with specific values from the diagram. Ex. 3: Why a Line Has Only One Slope 3-0 3 = Slope of BC 4-2 2 6-(-3) 9 3 = = Slope of AD 6-0 6 2

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