Homework: Similar Polygons with Dilation

Front

What are similar polygons?

Back

Polygons that have the same shape but may differ in size. Their corresponding angles are equal, and the lengths of corresponding sides are proportional.

Front

What is dilation in geometry?

Back

A transformation that alters the size of a figure but not its shape, defined by a center point and a scale factor.

Front

How do you determine if two triangles are similar?

Back

Two triangles are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.

Front

What is the scale factor in dilation?

Back

The ratio of the lengths of corresponding sides of the original figure to the dilated figure.

Front

If triangle SQV is dilated to triangle MNP, and QV = 15, what is NP if the scale factor is 1/3?

Back

NP = 5, since NP = QV * (1/3) = 15 * (1/3).

Front

What is the relationship between the sides of similar triangles?

Back

The ratios of the lengths of corresponding sides of similar triangles are equal.

Front

If two triangles have sides in the ratio 2:3, what is the scale factor from the smaller triangle to the larger triangle?

Back

The scale factor is 3/2.

Front

How do you find the missing variable in similar polygons?

Back

Set up a proportion using the lengths of corresponding sides and solve for the variable.

Front

If triangle ABC is similar to triangle DEF, and AB = 4, DE = 8, what is the scale factor?

Back

The scale factor is 8/4 = 2.

Front

What is the formula for finding the area of similar polygons?

Back

If the scale factor is k, the ratio of the areas is k^2.