Proportionality and Similar Shapes (7th TEKS)

Front

What does it mean for two figures to be similar?

Back

Two figures are similar if they have the same shape but not necessarily the same size. Their corresponding angles are equal, and the lengths of their corresponding sides are proportional.

Front

What is a scale factor in geometry?

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 triangles are similar, what can be said about their corresponding angles?

Back

The corresponding angles of similar triangles are equal.

Front

How do you find the length of a side in a similar figure using proportions?

Back

To find the length of a side in a similar figure, set up a proportion using the lengths of corresponding sides from the two figures and solve for the unknown length.

Front

What is the formula for calculating 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 a rectangle is dilated by a scale factor of 2, what happens to its dimensions?

Back

If a rectangle is dilated by a scale factor of 2, each dimension (length and width) is multiplied by 2, resulting in a rectangle that is twice as large in each direction.

Front

What is the relationship between the perimeters of similar figures?

Back

The ratio of the perimeters of similar figures is equal to the scale factor.

Front

How do you convert a map scale to actual distance?

Back

To convert a map scale to actual distance, multiply the length on the map by the scale factor to find the real-world distance.

Front

If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, what are the lengths of the sides of a similar triangle with a scale factor of 3?

Back

The lengths of the sides of the similar triangle would be 9 cm, 12 cm, and 15 cm (3 times each side).

Front

What is the definition of proportionality in mathematics?

Back

Proportionality refers to the relationship between two quantities where their ratio remains constant.