Solving 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

How do you find the length of a side in similar triangles?

Back

Use the proportion of the corresponding sides. If triangle ABC is similar to triangle DEF, then AB/DE = AC/DF = BC/EF.

Front

If triangle ABC is similar to triangle DEF, and AB = 4, DE = 8, what is the ratio of their areas?

Back

The ratio of their areas is the square of the ratio of their corresponding sides. (AB/DE)² = (4/8)² = 1/4.

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

If two triangles have sides in the ratio 3:5, what is the ratio of their perimeters?

Back

The ratio of their perimeters is also 3:5.

Front

What is a corresponding side in similar triangles?

Back

A side in one triangle that is proportional to a side in another triangle.

Front

If triangle ABC is similar to triangle DEF, and angle A = 30°, what is angle D?

Back

Angle D = 30° because corresponding angles in similar triangles are equal.