Similarity

Front

What is similarity in geometry?

Back

Similarity in geometry refers to the relationship between two 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 the similarity ratio?

Back

The similarity ratio is the ratio of the lengths of corresponding sides of two similar figures. It is a constant value that represents how much larger or smaller one figure is compared to the other.

Front

How do you determine if two triangles are similar?

Back

Two triangles are similar if they satisfy one of the following criteria: AA (Angle-Angle), SSS (Side-Side-Side), or SAS (Side-Angle-Side) similarity.

Front

What is the AA criterion for triangle similarity?

Back

The AA criterion states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What is the SSS criterion for triangle similarity?

Back

The SSS criterion states that if the lengths of the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What is the SAS criterion for triangle similarity?

Back

The SAS criterion 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 use proportions to find a missing side in similar triangles?

Back

To find a missing side in similar triangles, set up a proportion using the lengths of the corresponding sides and solve for the unknown side.

Front

If triangle ABC is similar to triangle DEF, and AB = 4, DE = 8, what is the ratio of their areas?

Back

The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides. Here, the ratio of the sides is 4:8 or 1:2, so the ratio of the areas is (1^2):(2^2) = 1:4.

Front

What is the relationship between the heights of similar triangles?

Back

The heights of similar triangles are in the same ratio as the lengths of their corresponding sides.

Front

How can you find the height of an object using similar triangles?

Back

To find the height of an object using similar triangles, create a right triangle with a known height and distance, and set up a proportion with the corresponding sides.