Similar Figures and Proportions Review

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 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 figures, it is the ratio of the lengths of corresponding sides.

Front

If two triangles are similar, what can be said about their angles?

Back

If two triangles are similar, their corresponding angles are equal.

Front

If the scale factor from ΔDEF to ΔABC is 1/2, what does this mean?

Back

It means that each side of ΔDEF is half the length of the corresponding side of ΔABC.

Front

How do you find the missing side of similar figures?

Back

To find the missing side, set up a proportion using the lengths of the corresponding sides of the similar figures.

Front

Solve for the missing side: If the sides of two similar triangles are in the ratio 2:5 and one side of the smaller triangle is 8, what is the corresponding side of the larger triangle?

Back

20 (Set up the proportion: 2/5 = 8/x, solve for x).

Front

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

Back

The ratio of their areas is equal to the square of the ratio of their corresponding side lengths.

Front

If the sides of two similar rectangles are in the ratio 3:4, what is the ratio of their areas?

Back

The ratio of their areas is 9:16 (3^2:4^2).

Front

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

Back

Area = 1/2 * base * height.

Front

If a triangle has a base of 10 and a height of 5, what is its area?

Back

Area = 1/2 * 10 * 5 = 25.