Similarity and Proportions

Front

What is the definition of similar polygons?

Back

Similar polygons are polygons that have the same shape but may differ in size. Their corresponding angles are equal, and the lengths of their corresponding sides are proportional.

Tags

CCSS.HSG.CO.B.6

CCSS.8.G.A.2

Front

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

Back

The corresponding angles of similar polygons are congruent.

Tags

CCSS.HSG.CO.B.6

CCSS.8.G.A.2

Front

What is the relationship between the sides of similar polygons?

Back

The lengths of the corresponding sides of similar polygons are proportional.

Tags

CCSS.HSG.CO.B.6

CCSS.8.G.A.2

Front

Solve for x: If two similar triangles have sides in the ratio 2:3 and one side of the smaller triangle is 4, what is the corresponding side in the larger triangle?

Back

x = 6 (Using the ratio 2/3 = 4/x, we find x = 6).

Front

What is a proportion in mathematics?

Back

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

Tags

CCSS.7.RP.A.2A

Front

Solve the proportion: 5/x = 10/20.

Back

x = 10 (Cross-multiplying gives 5 * 20 = 10 * x, so x = 10).

Tags

CCSS.7.RP.A.2C

Front

If the lengths of two similar figures are in the ratio 1:4, what is the ratio of their areas?

Back

The ratio of their areas is 1:16 (The area ratio is the square of the length ratio).

Front

What is the formula for finding the scale factor between two similar figures?

Back

The scale factor is found by dividing the length of a side of one figure by the corresponding side of the other figure.

Tags

CCSS.7.G.A.1

Front

Solve for x: The polygons are similar. If one side is 8 and the corresponding side is x, and the scale factor is 2:3, what is x?

Back

x = 12 (Using the scale factor 2/3 = 8/x, we find x = 12).

Tags

CCSS.7.G.A.1

Front

What does it mean for two ratios to be equivalent?

Back

Two ratios are equivalent if they represent the same relationship between quantities.

Tags

CCSS.6.RP.A.3A