Similarity

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Exploring the Properties of Similar Figures.

(A). Triangle EGH and triangle LME are similar. Find a sequence of translations, rotations, reflections, and dilations that shows this.

Describe the sequence of transformations you found.

(B). Hexagon ABCDEF and hexagon HGLKJI are similar. Find a sequence of translations, rotations, reflections, and dilations that shows this.

Describe the sequence of transformations you found.

(C). The same sequence of transformations takes Triangle A to Triangle B, takes Triangle B to Triangle C, and so on.

Describe a sequence of transformations with this property.

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Sketching Similar Figures.

(A). Sketch figures similar to Figure A that use only the transformations listed to show similarity using the applet below.

  1. A translation and a reflection. Label your sketch Figure B.
  2. A reflection and a dilation with scale factor greater than 1. Label your sketch Figure C.
  3. A rotation and a reflection. Label your sketch Figure D.
  4. A dilation with scale factor less than 1 and a translation. Label your sketch Figure E.

(B). The diagram has a pair of figures, one larger than the other. Show that the two figures are similar by identifying a sequence of translations, rotations, reflections, and dilations that takes the smaller figure to the larger one.

Describe the sequence of transformations you performed to take the smaller figure to the larger figure.

(C). The diagram has a pair of figures, one larger than the other. Show that the two figures are similar by identifying a sequence of translations, rotations, reflections, and dilations that takes the smaller figure to the larger one.

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Finding the Center of Dilation and Scale Factor Given Similar Shapes.

(A). Each figure shows a pair of similar triangles, one contained in the other. For each pair, describe a point and a scale factor to use for a dilation moving the larger triangle to the smaller one. Use a measurement tool to find the scale factor.

What point did you use for the center? What is the scale factor for moving the larger triangle to the smaller one?

(B). Each figure shows a pair of similar triangles, one contained in the other. For each pair, describe a point and a scale factor to use for a dilation moving the larger triangle to the smaller one. Use a measurement tool to find the scale factor.

What point did you use for the center? What is the scale factor for moving the larger triangle to the smaller one?

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 Find at least one way to show that triangle ABC and triangle DEF are similar.

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Here are two similar polygons. Measure the side lengths and angles of each polygon.

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The follwoing applet can be used to find out what similarity really is through dilations and rotations.

Which triangles can you get to lay perfectly over the gray one?