Similar figures and scale factor flashcard

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.

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 figures are similar, how do you find the missing side length?

Back

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

Front

If the scale factor is 3, what does that mean for the side lengths of similar figures?

Back

It means that each side length of the larger figure is 3 times the length of the corresponding side in the smaller figure.

Front

If the side of a smaller triangle is 4 cm and the scale factor is 2, what is the corresponding side in the larger triangle?

Back

The corresponding side in the larger triangle is 8 cm (4 cm x 2).

Front

What is the relationship between the angles of similar figures?

Back

The corresponding angles of similar figures are equal.

Front

How do you express the scale factor of two similar figures?

Back

The scale factor can be expressed as a ratio of the lengths of any two corresponding sides.

Front

If triangle A has sides of 5 cm, 12 cm, and 13 cm, and triangle B is similar to triangle A with a scale factor of 2, what are the side lengths of triangle B?

Back

The side lengths of triangle B are 10 cm, 24 cm, and 26 cm (5 cm x 2, 12 cm x 2, 13 cm x 2).

Front

What is the formula for finding the area of similar figures?

Back

The area of similar figures is proportional to the square of the scale factor. If the scale factor is k, then the ratio of the areas is k².

Front

If two similar rectangles have a scale factor of 1:4, how do their areas compare?

Back

The area of the larger rectangle is 16 times the area of the smaller rectangle (since 4² = 16).