Question

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.
drag and drop the correct card into the box.
use the ruler at the bottom of the card if you need help finding the scale factor. to access the ruler, click the
uler\ button and the ruler will appear. when you are finished using the ruler, click the
uler\ button and the ruler will disappear.

Explanation:

Step1: For the first pair of triangles \( \triangle ABC\) and \( \triangle A'BC'\)

The center of dilation is point \( B\).
Let's assume \( BA = 2BA'\) (by measuring or using the property of similar triangles). The scale factor \( k=\frac{BA'}{BA}\). If \( BA' = 1\) unit and \( BA=2\) units, then \( k = \frac{1}{2}\)

Step2: For the second pair of triangles \( \triangle DEF\) and \( \triangle D E'F'\)

The center of dilation is point \( D\).
Let's assume \( DE=2DE'\) (by measuring or using the property of similar triangles). The scale factor \( k=\frac{DE'}{DE}\). If \( DE' = 1\) unit and \( DE = 2\) units, then \( k=\frac{1}{2}\)

Answer:

For the first pair: Center \( B\), scale factor \( \frac{1}{2}\); For the second pair: Center \( D\), scale factor \( \frac{1}{2}\)