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Proportional Segments and Triangle Theorem Application

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This lesson focuses on using properties of similar triangles to solve proportionality and triangle angle bisector theorems. Examples include finding segment lengths and verifying parallel segments. A real-life art application is also explored. Assignment problems provided.

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Proportional Segments and Triangle Theorem Application

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  1. Warm Up Solve each proportion. 1.2. 3.4.

  2. Objectives Use properties of similar triangles to find segment lengths. Apply proportionality and triangle angle bisector theorems.

  3. It is given that , so by the Triangle Proportionality Theorem. Example 1: Finding the Length of a Segment Find US.

  4. Verify that . Example 2: Verifying Segments are Parallel

  5. Example 3: Art Application Suppose that an artist decided to make a larger sketch of the trees. In the figure, if AB = 4.5 in., BC = 2.6 in., CD = 4.1 in., and KL = 4.9 in., find LM and MN to the nearest tenth of an inch.

  6. The previous theorems and corollary lead to the following conclusion.

  7. Example 4: Using the Triangle Angle Bisector Theorem Find PS and SR.

  8. Assignment Pg. 498 (1-20, 26-27)

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