Triangle Proportionality

Front

What is Triangle Proportionality?

Back

Triangle Proportionality 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 is 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 into segments that are proportional.

Front

How do you determine if two triangles are similar?

Back

Two triangles are similar if their corresponding angles are equal or their corresponding sides are in proportion.

Front

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

Back

The ratio of their corresponding sides is 1:2.

Front

What is the formula for finding the length of a side in similar triangles?

Back

If triangle ABC is similar to triangle DEF, then (AB/DE) = (BC/EF) = (AC/DF).

Front

If a triangle has sides of lengths 3, 4, and 5, is it a right triangle?

Back

Yes, it is a right triangle because it follows the Pythagorean theorem: 3² + 4² = 5².

Front

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

Back

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

Front

If the sides of triangle XYZ are in the ratio 2:3, what is the ratio of the areas of triangle XYZ to triangle ABC if the sides of triangle ABC are in the ratio 3:4?

Back

The ratio of the areas is (2/3)² : (3/4)² = 4/9 : 9/16.

Front

What is the Angle-Angle (AA) criterion for triangle similarity?

Back

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