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# Common Core Standards: Math

# Math.CCSS.Math.Content.HSG-SRT.A.1

**1. Verify experimentally the properties of dilations given by a center and a scale factor:**

Your students may understand generally what the term similar means, but it can be very specific when it comes to geometry. For instance, while Tia and Tamera Mowry are very similar (you know, since they're identical twins and all), they aren't geometrically similar. How on earth could that be?

In geometry, **similar** objects are exactly the same *shape*, but not necessarily the same *size*. So one object could be smaller than a pea and another could be larger than Antarctica, but if they have the exact same shape, they're similar. How curious.

Still, the idea of being "exactly the same shape" is a little vague. How can we be sure that two objects of different sizes still have the same shape? That's where dilations, centers, and scale factors come in.

#### Standard Components

- A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
- The dilation of a line segment is longer or shorter in the ratio given by the scale factor.