Proportions and Similar Figures

Front

What does it mean for two figures to be similar?

Back

Two figures are similar if they have the same shape but not necessarily the same size, meaning their corresponding angles are equal and their corresponding sides are in proportion.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal.

Front

How do you solve a proportion?

Back

To solve a proportion, you can use cross-multiplication, where you multiply the numerator of one ratio by the denominator of the other ratio and set the two products equal to each other.

Front

What is the ratio of two quantities?

Back

A ratio is a comparison of two quantities, showing how many times one value contains or is contained within the other.

Front

How can you simplify a ratio?

Back

To simplify a ratio, divide both terms of the ratio by their greatest common divisor (GCD).

Front

What is the relationship between similar figures and their corresponding sides?

Back

In similar figures, the lengths of corresponding sides are proportional.

Front

If two similar triangles have sides of lengths 3 cm and 5 cm, what is the ratio of their areas?

Back

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths. Therefore, (3/5)² = 9/25.

Front

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

Back

The area of a triangle can be found using the formula: Area = 1/2 * base * height.

Front

What is a scale factor in similar figures?

Back

The scale factor is the ratio of the lengths of corresponding sides of two similar figures.

Front

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

Back

To find the scale factor, divide the length of a side of one figure by the length of the corresponding side of the other figure.