Geometry Chapter 7: Similarity

Front

What is the definition of similar triangles?

Back

Similar triangles are triangles that have the same shape but may differ in size. Their corresponding angles are equal, and the lengths of their corresponding sides are proportional.

Front

What is the criteria for determining 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).

Front

If two triangles are similar, how do you find the length of an unknown side?

Back

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

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

How do 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 scale factor in similar triangles?

Back

The scale factor is the ratio of the lengths of corresponding sides of two similar triangles.

Front

If triangle ABC is similar to triangle DEF, and the lengths of sides AB and DE are 4 cm and 8 cm respectively, what is the scale factor?

Back

The scale factor is 1:2.

Front

How do you solve for a missing side length in similar triangles?

Back

Set up a proportion using the known side lengths and cross-multiply to solve for the missing side length.

Front

What is the significance of 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, the triangles are similar.

Front

In a triangle with sides measuring 11 cm, 16 cm, and 16 cm, what is the ratio of the sides to a similar triangle with one side measuring 24 cm?

Back

The ratio of the sides is 11:24, 16:24, and 16:24.