Similar Shapes, Scale Factors, and Missing Side Lengths - 6

Front

What are similar shapes?

Back

Shapes that have the same shape but different sizes. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

What is a scale factor?

Back

A number that scales, or multiplies, some quantity. In similar shapes, it is the ratio of the lengths of corresponding sides.

Front

If two triangles are similar and the scale factor is 2, what does that mean?

Back

It means that each side of the second triangle is twice as long as the corresponding side of the first triangle.

Front

How do you find the missing side length in similar shapes?

Back

Use the scale factor to set up a proportion between the corresponding sides of the shapes.

Front

If the length of a side in the first triangle is 3 and the corresponding side in the second triangle is 6, what is the scale factor?

Back

The scale factor is 2.

Front

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

Back

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

Front

If the scale factor between two similar triangles is 3, how many times greater is the area of the second triangle compared to the first?

Back

The area of the second triangle is 9 times greater than the first (3^2 = 9).

Front

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

Back

Area = 1/2 * base * height.

Front

If the area of the first triangle is 12 square units, what is the area of the second triangle if the scale factor is 1/3?

Back

The area of the second triangle is 12 * (1/3)^2 = 12 * 1/9 = 4/3 square units.

Front

What does it mean if the area of the second hexagon is 2.25 times greater than the first?

Back

It means that the area of the second hexagon is 2.25 times the area of the first hexagon.