Triangle Proportionality Theorem Practice

Front

What is the Triangle Proportionality Theorem?

Back

The Triangle Proportionality Theorem states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

Front

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

Back

The corresponding sides of similar triangles are in proportion.

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, meaning all corresponding sides and angles are equal.

Front

Solve for x: If a line parallel to one side of a triangle divides the other two sides into segments of lengths 3 and x, and 5 and 15, what is x?

Back

x = 5.

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

If triangle ABC is similar to triangle DEF, and the length of side AB is 6 and side DE is 9, what is the ratio of their corresponding sides?

Back

The ratio of their corresponding sides is 6:9 or 2:3.

Front

Find the missing length indicated: If a triangle has sides of lengths 10, 15, and x, and is similar to another triangle with sides of lengths 20, 30, and 2x, what is x?

Back

x = 10.

Front

What is the significance of the Side-Splitter Theorem?

Back

The Side-Splitter Theorem states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

Front

If two triangles have a ratio of 1:4 for their corresponding sides, what is the ratio of their areas?

Back

The ratio of their areas is 1:16.

Front

Solve for x: If a triangle has sides of lengths 4, 8, and x, and is similar to another triangle with sides of lengths 2, 4, and 1, what is x?

Back

x = 2.