## Standards

1. Verify experimentally the properties of dilations with given center and scale factor:

- When a line segment passes through the center of dilation, the line segment and its image lie on the same line. When a line segment does not pass through the center of dilation, the line segment and its image are parallel.
- The length of the image of a line segment is equal to the length of the line segment multiplied by the scale factor.
- The distance between the center of a dilation and any point on the image is equal to the scale factor multiplied by the distance between the dilation center and the corresponding point on the pre-image.
- Dilations preserve angle measure.

- Determine whether two figures are similar by specifying a sequence of transformations that will transform one figure into the other.
- Use the properties of dilations to show that two triangles are similar when all corresponding pairs of sides are proportional and all corresponding pairs of angles are congruent.

4. Use similarity to solve problems and to prove theorems about triangles. Use theorems about triangles to prove relationships in geometric figures:

- A line parallel to one side of a triangle divides the other two sides proportionally and its converse.
- The Pythagorean Theorem

## Schedule## Resources |
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