Similarity & Proportions

Front

What is similarity in geometry?

Back

Similarity in geometry refers to the property of two shapes being the same in shape but not necessarily in size. This means that their corresponding angles are equal and their corresponding sides are in proportion.

Front

What is the similarity statement for two similar triangles?

Back

The similarity statement for two similar triangles can be written as ΔABC ~ ΔDEF, indicating that triangle ABC is similar to triangle DEF.

Front

What are the criteria for triangle similarity?

Back

The criteria for triangle similarity include: 1. AA (Angle-Angle) similarity: If two angles of one triangle are equal to two angles of another triangle, the triangles are similar. 2. SAS (Side-Angle-Side) similarity: If two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, the triangles are similar. 3. SSS (Side-Side-Side) similarity: If the corresponding sides of two triangles are in proportion, the triangles are similar.

Front

How do you find the missing side length in similar polygons?

Back

To find the missing side length in similar polygons, set up a proportion using the lengths of corresponding sides. For example, if polygon A has a side length of 5 and polygon B has a corresponding side length of x, and the ratio of their sides is known, you can solve for x.

Front

If two triangles have sides of lengths 3, 4, and 5, and 6, 8, and 10, are they similar?

Back

Yes, the triangles are similar because the sides are in proportion (3:6 = 1:2, 4:8 = 1:2, 5:10 = 1:2).

Front

What is the ratio of similarity?

Back

The ratio of similarity is the ratio of the lengths of corresponding sides of two similar figures. It can be expressed as a fraction or a decimal.

Front

If triangle ABC is similar to triangle DEF, and the length of side AB is 4 cm and side DE is 8 cm, what is the ratio of similarity?

Back

The ratio of similarity is 1:2, since 4 cm (AB) to 8 cm (DE) simplifies to 1:2.

Front

What does it mean if two polygons are not similar?

Back

If two polygons are not similar, it means that their corresponding angles are not equal or their corresponding sides are not in proportion.

Front

How can you prove that two triangles are similar using the AA criterion?

Back

To prove that two triangles are similar using the AA criterion, show that two angles of one triangle are equal to two angles of another triangle. If this is true, the triangles are similar.

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.