Similar Figures & Scale Factor

Front

What are similar figures?

Back

Similar figures are shapes that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, some quantity. In the context of similar figures, it is the ratio of the lengths of corresponding sides.

Front

If two triangles have a scale factor of 2, what does that mean?

Back

It means that each side of the larger triangle is twice the length of the corresponding side of the smaller triangle.

Front

How do you determine if two figures are similar?

Back

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

Front

What is the measure of angle X if two similar triangles have angles of 60 degrees?

Back

Angle X measures 60 degrees.

Front

If a triangle has sides of 6, 8, and 10, what are the corresponding sides of a similar triangle with a scale factor of 2?

Back

The corresponding sides would be 12, 16, and 20.

Front

What happens to the size of a shape when the scale factor is greater than 1?

Back

The shape gets larger.

Front

What happens to the size of a shape when the scale factor is less than 1?

Back

The shape gets smaller.

Front

If two figures are similar and one has a scale factor of 1.5, what is the ratio of their areas?

Back

The ratio of their areas is the square of the scale factor, which is 1.5^2 = 2.25.

Front

Are two triangles with sides of 3, 4, and 5 similar to triangles with sides of 6, 8, and 10?

Back

Yes, they are similar because the sides are in proportion (scale factor of 2).