Similarity

Front

What is similarity in geometry?

Back

Similarity in geometry refers to the relationship between two figures that have the same shape but may differ in size. The corresponding angles are equal, and the lengths of corresponding sides are proportional.

Front

What does SSS~ stand for?

Back

SSS~ stands for 'Side-Side-Side Similarity', which states that if the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What does AA~ stand for?

Back

AA~ stands for 'Angle-Angle Similarity', which states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What does SAS~ stand for?

Back

SAS~ stands for 'Side-Angle-Side Similarity', which states that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

How do you solve a proportion?

Back

To solve a proportion, cross-multiply the terms and set the products equal to each other. For example, if a/b = c/d, then ad = bc.

Front

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

Back

If two triangles are similar, the lengths of their corresponding sides are in proportion.

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

How can you determine if two triangles are not similar?

Back

Two triangles are not similar if their corresponding angles are not equal or if the ratios of their corresponding sides are not equal.

Front

What is the missing side if two similar triangles have sides of 9 and x, and the corresponding sides are in the ratio of 3:7?

Back

x = 21 (since 9/3 = x/7, cross-multiply to find x).

Front

What is the similarity statement for triangles ΔABC and ΔDEF if they are similar by AA~?

Back

ΔABC ∼ ΔDEF.