Similar shapes and scale factor

Front

What is the definition of similar shapes?

Back

Similar shapes are figures that have the same shape but may differ in size. Their corresponding angles are equal, and their 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 shapes, it is the ratio of the lengths of corresponding sides.

Front

If the scale factor is 2, what happens to the size of the figure?

Back

The figure is enlarged to twice its original size.

Front

If the scale factor is 0.5, what happens to the size of the figure?

Back

The figure is reduced to half its original size.

Front

What does it mean for two figures to be proportional?

Back

Two figures are proportional if their corresponding sides are in the same ratio.

Front

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

Back

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

Front

If triangle A has sides of 4, 6, and 8, and triangle B has sides of 8, 12, and 16, are the triangles similar?

Back

Yes, triangle A and triangle B are similar because the sides are in proportion (2:1 ratio).

Front

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

Back

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

Front

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

Back

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

Front

What is the formula for finding the area of a triangle?

Back

Area = 1/2 * base * height.