Here are Circles \(c\) and \(d\). Point \(O\) is the center of dilation, and the dilation takes Circle \(c\) to Circle \(d\).

1. Plot a point on Circle \(c\). Label the point \(P\). Plot where \(P\) goes when the dilation is applied and label the point \(P'\).
2. Plot a point on Circle \(d\). Label the point \(Q'\). Plot the point that the dilation takes to \(Q'\) and label it \(Q\).

Here is triangle \(ABC\).

1. Dilate each vertex of triangle \(ABC\) using \(P\) as the center of dilation and a scale factor of 2. Draw the triangle connecting the 3 new points.
2. Dilate each vertex of triangle \(ABC\) using \(P\) as the center of dilation and a scale factor of \(\frac 1 2\). Draw the triangle connecting the 3 new points.

3. Measure the longest side of each of the 3 triangles. What do you notice?

4. Measure the angles of each triangle. What do you notice?

The line has been partitioned into 3 angles.

A straight line with two rays coming out of a single point. One slanting up and to the left. One slanting up and to the right. Three angles are formed. 39 degrees. 99 degrees. 42 degrees.

Is there a triangle with these 3 angle measures? Explain.