Similarity Through Dilations

Similarity Through Dilations

A dilation changes the size of a figure while keeping its shape the same. In a similarity problem, the key idea is that corresponding side lengths are multiplied by the same scale factor.

1. Identify the center and scale factor

Look for the point of dilation and determine whether the figure is enlarged or reduced. If you are given matching lengths, compare them to find the scale factor:

• new length ÷ original length
• or original length ÷ new length, depending on the direction of the change

2. Match corresponding parts

Make sure you compare the correct sides, angles, or points. Angles stay equal under dilation, and side lengths change proportionally.

3. Solve using proportional relationships

If a side length is missing, set up a proportion with a known pair of corresponding sides. Multiply carefully and simplify the final result.

4. Check your answer

Your answer should preserve the shape’s proportional structure. Verify that all corresponding side lengths use the same scale factor and that your simplified result is consistent with enlargement or reduction.

If the problem asks for an exact answer, leave it in exact form after simplifying.