Similarity & Proportions

Front

What does it mean for two triangles to be similar?

Back

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

Front

What is the scale factor in similar figures?

Back

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

Front

If triangle A is similar to triangle B, and the length of a side in triangle A is 4 cm, and the corresponding side in triangle B is 8 cm, what is the scale factor from A to B?

Back

The scale factor from triangle A to triangle B is 1:2.

Front

How do you find a missing length in similar triangles?

Back

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

Front

If triangle X has sides of lengths 3, 4, and 5, and triangle Y is similar to triangle X with a scale factor of 2, what are the lengths of the sides of triangle Y?

Back

The lengths of the sides of triangle Y are 6, 8, and 10.

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 side lengths.

Front

If the scale factor of two similar polygons is 3:5, what is the ratio of their areas?

Back

The ratio of their areas is 9:25.

Front

How do you solve for a variable in similar triangles?

Back

Set up a proportion based on the lengths of corresponding sides and solve for the variable.

Front

If two similar triangles have a scale factor of 1:3, and the shorter side of the smaller triangle is 5 cm, what is the length of the corresponding side in the larger triangle?

Back

The length of the corresponding side in the larger triangle is 15 cm.

Front

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

Back

Area = 1/2 * base * height.