Similar Polygons

Front

What are similar polygons?

Back

Polygons that have the same shape but not necessarily the same size. Their corresponding angles are equal, and the lengths of their corresponding sides are proportional.

Front

What is the scale factor in similar polygons?

Back

The ratio of the lengths of corresponding sides of two similar polygons.

Front

If two triangles are similar, how do you find the length of a side in one triangle if you know the corresponding side in the other triangle?

Back

Use the scale factor: if the scale factor is k, then the length of the side in the second triangle is the length in the first triangle multiplied by k.

Front

If triangle A has sides of lengths 3, 4, and 5, and triangle B is similar to triangle A with a scale factor of 2, what are the lengths of the sides of triangle B?

Back

The lengths of the sides of triangle B are 6, 8, and 10.

Front

How do you determine if two polygons are similar?

Back

Check if their corresponding angles are equal and the lengths of their corresponding sides are proportional.

Front

What is the relationship between the areas of two similar polygons?

Back

The ratio of their areas is equal to the square of the scale factor.

Front

If the scale factor of two similar polygons is 3, what is the ratio of their areas?

Back

The ratio of their areas is 3^2 = 9.

Front

If triangle XYZ is similar to triangle ABC and the length of side XY is 6 and the length of side AB is 9, what is the scale factor from triangle XYZ to triangle ABC?

Back

The scale factor is 9/6 = 1.5.

Front

What does it mean if two polygons are not similar?

Back

It means that their corresponding angles are not equal or their corresponding sides are not proportional.

Front

If the lengths of corresponding sides of two similar polygons are 4 cm and 8 cm, what is the scale factor from the smaller to the larger polygon?

Back

The scale factor is 8/4 = 2.