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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.**

- A translation and a reflection. Label your sketch Figure B.
- A reflection and a dilation with scale factor greater than 1. Label your sketch Figure C.
- A rotation and a reflection. Label your sketch Figure D.
- 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?

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