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 the lengths of corresponding sides are proportional.

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 are similar with a scale factor of 2, what does this mean?

Back

It means that each side of one triangle is twice as long as the corresponding side of the other triangle.

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 happens to the area of a shape when the scale factor is increased?

Back

The area of a shape increases by the square of the scale factor. For example, if the scale factor is 2, the area increases by a factor of 2^2 = 4.

Front

What is the relationship between the scale factor and the size of the shape?

Back

If the scale factor is greater than 1, the shape gets larger. If the scale factor is less than 1, the shape gets smaller.

Front

If triangle A has sides of length 6, 8, and 10, and triangle B is similar with a scale factor of 3, what are the lengths of the sides of triangle B?

Back

The sides of triangle B will be 18, 24, and 30 (6*3, 8*3, 10*3).

Front

What does it mean for sides to 'correspond' in similar figures?

Back

Corresponding sides in similar figures are the sides that are in the same relative position in each figure.

Front

If triangle A has a side of length 5 and triangle B has a corresponding side of length 10, what is the scale factor?

Back

The scale factor is 2 (10/5).

Front

How can you find the missing side of a similar triangle?

Back

You can find the missing side by setting up a proportion using the lengths of the corresponding sides of the similar triangles.