Proportions and Similar Triangles

Front

What is a proportion?

Back

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

Front

How do you solve for a variable in a proportion?

Back

To solve for a variable in a proportion, cross-multiply and then isolate the variable.

Front

What is the relationship between similar triangles?

Back

Similar triangles have the same shape but may differ in size; their corresponding angles are equal, and their corresponding sides are in proportion.

Front

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

Back

The lengths of their corresponding sides are proportional.

Front

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

Back

The scale factor is the ratio of the lengths of any two corresponding sides of the triangles.

Front

How do you set up a proportion to find an unknown length in similar triangles?

Back

Set up a proportion using the lengths of corresponding sides from the two triangles.

Front

What is the cross-multiplication method?

Back

Cross-multiplication is a method used to solve proportions by multiplying the numerator of one ratio by the denominator of the other ratio.

Front

If the ratio of dogs to cats in a shelter is 5:3 and there are 25 dogs, how many cats are there?

Back

c = 15 (Set up the proportion 5/3 = 25/c and solve for c).

Front

What is the definition of similar figures?

Back

Similar figures are shapes that have the same form but may differ in size, maintaining proportional dimensions.

Front

How can you determine if two triangles are similar?

Back

Two triangles are similar if their corresponding angles are equal or if the lengths of their corresponding sides are proportional.