Similarity & Proportions

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 similarity criterion?

Back

The AA (Angle-Angle) 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 SAS similarity criterion?

Back

The SAS (Side-Angle-Side) similarity criterion states that if one angle of a triangle is equal to one angle of another triangle and the sides including those angles are in proportion, then the triangles are similar.

Front

What is the SSS similarity criterion?

Back

The SSS (Side-Side-Side) similarity criterion states that if the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

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

Back

The ratio of their corresponding sides is 1:2.

Front

Solve for x: If triangle XYZ is similar to triangle PQR, and the lengths of XY = 6 cm, YZ = x cm, and PR = 12 cm, find x.

Back

x = 12 cm.

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 sides.

Front

If the sides of triangle ABC are 3 cm, 4 cm, and 5 cm, and triangle DEF is similar to triangle ABC with a side length of 6 cm, what is the length of the corresponding side in triangle DEF?

Back

The corresponding side in triangle DEF is 8 cm.

Front

State whether the following triangles are similar: Triangle GHI with angles 30°, 60°, 90° and Triangle JKL with angles 30°, 60°, 90°. Justify your answer.

Back

Yes, they are similar by AA similarity criterion.

Front

If two triangles have a similarity ratio of 3:5, what is the ratio of their areas?

Back

The ratio of their areas is 9:25.