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Proportional Segments and Triangle Theorem Application

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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