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Use properties of similar triangles to find segment lengths.

Learn how artists employ mathematical techniques mimicking real-life sight for depth perception in paintings. See examples of applying similar triangles, proportionality theorems and angle bisector theorems in art. Explore various dimensional perspectives.

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Use properties of similar triangles to find segment lengths.

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

  2. Artists use mathematical techniques to make two-dimensional paintings appear three-dimensional. The invention of perspective was based on the observation that far away objects look smaller and closer objects look larger. Mathematical theorems like the Triangle Proportionality Theorem are important in making perspective drawings.

  3. Example 1a: Finding the Length of a Segment Find US.

  4. Check It Out! Example 1b Find PN.

  5. Verify that . Example 2a: Verifying Segments are Parallel

  6. AC = 36 cm, and BC = 27 cm. Verify that . Check It Out! Example 2b

  7. Example 3a: 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.

  8. Check It Out! Example 3b Use the diagram to find LM and MN to the nearest tenth.

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

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

  11. Check It Out! Example 4b Find AC and DC.

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