Honors Geometry - Using Similarity Criteria

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 AA (Angle-Angle) similarity criterion?

Back

The AA similarity 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 (Side-Side-Side) similarity criterion?

Back

The SSS similarity 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 (Side-Angle-Side) similarity criterion?

Back

The SAS similarity 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

If triangle ABC is similar to triangle DEF, and the lengths of AB and DE are 4 and 8 respectively, what is the ratio of their corresponding sides?

Back

The ratio of their corresponding sides is 1:2.

Front

How do you find the missing length in similar triangles?

Back

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

Front

If two triangles are similar and one triangle has a side length of 10, and the corresponding side in the other triangle is 15, what is the scale factor?

Back

The scale factor is 3:2.

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.

Front

If triangle XYZ is similar to triangle PQR, and the area of triangle XYZ is 36 square units, what is the area of triangle PQR if the scale factor is 2?

Back

The area of triangle PQR is 144 square units.

Front

What is the formula for finding the length of a side in similar triangles?

Back

If triangle ABC is similar to triangle DEF, then (AB/DE) = (BC/EF) = (AC/DF).