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

Back

Yes, triangle A and triangle B are similar because their corresponding sides are in proportion (3:6, 4:8, 5:10).

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

If two triangles are similar, what can be said about their areas?

Back

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Front

If triangle A is similar to triangle B and the length of a side of triangle A is 5 cm, and the corresponding side of triangle B is 10 cm, what is the ratio of their sides?

Back

The ratio of their sides is 1:2.

Front

What is the measure of angle b if triangle A has angles 36°, 64°, and b?

Back

Angle b measures 80° (since the sum of angles in a triangle is 180°).

Front

If triangle A has angles 30°, 60°, and 90°, what are the angles of a similar triangle?

Back

The angles of a similar triangle will also be 30°, 60°, and 90°.