similarity and scale factor

Front

What is similarity in geometry?

Back

Similarity in geometry refers to two 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 geometry, it is the ratio of the lengths of two corresponding sides of similar figures.

Front

If a triangle has a perimeter of 36 units and is scaled down by a factor of 1/2, what is the new perimeter?

Back

The new perimeter is 18 units.

Front

How do you find the scale factor between two similar triangles?

Back

To find the scale factor, divide the length of a side of the larger triangle by the length of the corresponding side of the smaller triangle.

Front

If the scale factor from triangle A to triangle B is 3/2, what does this mean?

Back

This means that triangle B is 1.5 times larger than triangle A.

Front

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

Back

The ratio of the areas of two similar figures is equal to the square of the scale factor.

Front

If the scale factor is 1/4, what is the ratio of the areas of the two similar triangles?

Back

The ratio of the areas is 1/16.

Front

What happens to the dimensions of a shape if the scale factor is greater than 1?

Back

If the scale factor is greater than 1, the shape enlarges.

Front

What happens to the dimensions of a shape if the scale factor is less than 1?

Back

If the scale factor is less than 1, the shape shrinks.

Front

If triangle A has sides of length 4, 6, and 8, and triangle B is similar to triangle A with a scale factor of 1/2, what are the lengths of the sides of triangle B?

Back

The sides of triangle B are 2, 3, and 4.