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Using Similar Triangles

Using Similar Triangles. Butterflies, Pinwheels and Wallpaper 4.4. Learning Goal 1 (8.G.A.3 & 4): The student will understand and use informal arguments to prove congruency and similarity using physical models, transparencies or geometry software. Similar Triangles.

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Using Similar Triangles

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  1. Using Similar Triangles Butterflies, Pinwheels and Wallpaper 4.4

  2. Learning Goal 1 (8.G.A.3 & 4): The student will understand and use informal arguments to prove congruency and similarity using physical models, transparencies or geometry software.

  3. Similar Triangles • Similar triangles have the same shape, but are usually a different size. • You can use the relationships between corresponding parts of similar triangles to solve measurement problems.

  4. Similar Triangles • The diagram shows a method for calculating the height of an object that is difficult to measure directly. • Place a mirror on a leveled spot at a convenient distance from the object. • Back up from the mirror until you see the reflection of the top of the object in the center of the mirror.

  5. The two triangles in the diagram are similar. • To find the object’s height, you need to measure three distances and use similar triangles. • What distances do you think we should measure? Person’s height Object’s distance to mirror. Person’s distance to mirror.

  6. What do you do next? • Once you have these three measurements, how do you find the height of the traffic light? • Set up a proportion and solve for the missing height. 160 cm 600 cm 200 cm

  7. Set up and solve the proportion • Height of object = Height of personDistance of object to mirror Distance of person to mirror. • x = 160600 200 200x = 600(160) 200x = 96,000 x = 480 The height of the traffic light is 480 cm. 160 cm 600 cm 200 cm

  8. Labsheet 4.4

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