Similar Triangles

Front

What are similar triangles?

Back

Triangles that have the same shape but may have different sizes. 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 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 a missing side?

Back

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

Front

If triangle XYZ has sides of lengths 6, 8, and 10, and triangle PQR is similar to triangle XYZ with a side length of 12, what is the length of the corresponding side in triangle PQR?

Back

The corresponding side in triangle PQR is 16.

Front

What is the relationship between the areas of two similar triangles?

Back

The ratio of their areas is equal to the square of the ratio of their corresponding side lengths.

Front

If the sides of triangle A are 3, 4, and 5, and the sides of triangle B are 6, 8, and 10, are the triangles similar?

Back

Yes, triangle A and triangle B are similar because their corresponding sides are in proportion (1:2).

Front

How do you determine if two triangles are similar using their angles?

Back

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