Similar Figures/Triangles/Theorem

Front

What postulate proves that two triangles are similar if two sides are proportional and the included angle is equal?

Back

SAS (Side-Angle-Side) Postulate.

Front

The Angle-Angle Similarity (AA ~) Theorem states if two angles of one triangle are ____________ to two angles of another triangle, then the triangles are _____________.

Back

congruent; similar.

Front

If two figures are similar, what can be said about their corresponding sides?

Back

The corresponding sides are proportional.

Front

Using a proportion, if a tree's shadow is 4 ft and a 16 ft tall person casts a shadow of 2 ft, what is the height of the tree?

Back

x = 16 ft.

Front

If two similar triangles have sides in the ratio of 2:5, what is the ratio of their areas?

Back

The ratio of their areas is 4:25.

Front

What is the definition of similar figures?

Back

Similar figures have the same shape but not necessarily the same size; their corresponding angles are equal and their corresponding sides are proportional.

Front

What theorem states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar?

Back

Angle-Angle (AA) Similarity Theorem.

Front

If triangle ABC is similar to triangle DEF, and the length of side AB is 6 cm and side DE is 15 cm, what is the scale factor from triangle ABC to triangle DEF?

Back

The scale factor is 2.5.

Front

What is the relationship between the lengths of corresponding sides of similar triangles?

Back

The lengths of corresponding sides of similar triangles are in proportion.

Front

If the sides of triangle XYZ are 3 cm, 4 cm, and 5 cm, and triangle PQR is similar to triangle XYZ with a scale factor of 3, what are the lengths of the sides of triangle PQR?

Back

The sides of triangle PQR are 9 cm, 12 cm, and 15 cm.