Similar Triangles

Front

What are similar triangles?

Back

Triangles 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 Angle-Angle (AA) similarity criterion?

Back

If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What is the Side-Side-Side (SSS) similarity criterion?

Back

If the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What is the Side-Angle-Side (SAS) similarity criterion?

Back

If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in proportion, then the triangles are similar.

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 ratio of their corresponding sides?

Back

The ratio of their corresponding sides is 1:2.

Front

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

Back

Use the proportion of the lengths of corresponding sides to set up a ratio and solve for the unknown side.

Front

What is the formula for finding the area ratio of two similar triangles?

Back

The area ratio is the square of the ratio of their corresponding sides.

Front

If triangle XYZ has sides of lengths 3 cm, 4 cm, and 5 cm, and triangle PQR is similar to triangle XYZ, what are the lengths of the sides of triangle PQR if the shortest side is 6 cm?

Back

The sides of triangle PQR are 6 cm, 8 cm, and 10 cm.

Front

Solve for x: If triangle ABC is similar to triangle DEF, and AB = 6 cm, DE = x cm, and the ratio of sides is 2:3, what is x?

Back

x = 9 cm.

Front

If the lengths of two corresponding sides of similar triangles are 5 cm and 15 cm, what is the scale factor?

Back

The scale factor is 1:3.