Similar Figures - Find the Missing Side

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 their corresponding sides are in proportion.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. It is often used to solve problems involving similar figures.

Front

How do you set up a proportion to find a missing side in similar figures?

Back

To set up a proportion, you compare the ratios of the corresponding sides of the similar figures. For example, if figure A has a side of length a and figure B has a corresponding side of length b, and you need to find the missing side x in figure B, you can set up the proportion: a/b = x/c, where c is the corresponding side in figure A.

Tags

CCSS.HSG.SRT.A.2

Front

If two triangles are similar, what can you say about their angles?

Back

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

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

If triangle ABC is similar to triangle DEF, and the length of side AB is 4 cm and side DE is 8 cm, what is the ratio of their sides?

Back

The ratio of their sides is 4:8, which simplifies to 1:2.

Tags

CCSS.HSG.SRT.A.2

Front

What is the missing side if triangle ABC is similar to triangle DEF, AB = 4 cm, DE = 8 cm, and BC = 6 cm?

Back

The missing side EF can be found using the proportion: 4/8 = 6/EF. Solving gives EF = 12 cm.

Tags

CCSS.HSG.SRT.A.2

Front

What is the scale factor between two similar figures?

Back

The scale factor is the ratio of the lengths of corresponding sides of two similar figures. It indicates how much one figure has been enlarged or reduced compared to the other.

Tags

CCSS.7.G.A.1

Front

If the scale factor of two similar rectangles is 3:5, and the shorter side of the smaller rectangle is 9 cm, what is the length of the corresponding side in the larger rectangle?

Back

To find the length of the corresponding side, set up the proportion: 9/length = 3/5. Solving gives length = 15 cm.

Tags

CCSS.7.G.A.1

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 ratio of their corresponding sides.

Front

If the ratio of the sides of two similar triangles is 2:3, what is the ratio of their areas?

Back

The ratio of their areas is 2^2:3^2, which simplifies to 4:9.