Unit 7 Proportions and Similarities Review

Front

What is a similarity statement in geometry?

Back

A similarity statement indicates that two figures are similar, meaning they have the same shape but not necessarily the same size. It is denoted using the symbol '~'. For example, ΔABC ~ ΔDEF means triangle ABC is similar to triangle DEF.

Front

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

Back

The corresponding sides of similar triangles are in proportion, meaning the ratios of the lengths of corresponding sides are equal.

Front

What does the symbol '~' represent in geometry?

Back

The symbol '~' represents similarity between two geometric figures.

Front

If ABCD ~ HIJK, what can be inferred about the angles of the two shapes?

Back

The corresponding angles of similar shapes are equal.

Front

How do you find the length of a side in similar triangles?

Back

To find the length of a side in similar triangles, set up a proportion using the lengths of corresponding sides from the two triangles.

Front

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

Back

The perimeter of a triangle is found by adding the lengths of all three sides: P = a + b + c.

Front

If the perimeter of triangle ABC is 36, what is the perimeter of triangle DEF if they are similar and the ratio of their sides is 2:1?

Back

The perimeter of triangle DEF would be 18, since the perimeter is proportional to the sides.

Front

What is a proportion in mathematics?

Back

A proportion is an equation that states that two ratios are equal. For example, if a/b = c/d, then a, b, c, and d are in proportion.

Front

How can you solve for a missing side in a proportion?

Back

To solve for a missing side in a proportion, cross-multiply and then divide. For example, if a/b = c/x, then x = (b*c)/a.

Front

What is the relationship between the areas of two similar triangles?

Back

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths.