Triangle Proportionality Theorems

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 a line segment divides two sides of a triangle proportionally, what can be concluded about the line segment?

Back

The line segment is parallel to the third side of the triangle.

Front

How do you find the missing length in a triangle using proportionality?

Back

Set up a proportion based on the lengths of the sides and solve for the missing length.

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 * base * height.

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 significance of the ratio of the sides in similar triangles?

Back

The ratio of the sides of similar triangles is equal to the ratio of their corresponding altitudes.

Front

If triangle ABC is similar to triangle DEF, and AB = 4, AC = 6, and DE = 8, what is the length of DF?

Back

DF = 12 (using the ratio of similarity: 4/8 = 6/x).

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if their corresponding sides and angles are equal.

Front

How can you determine if two triangles are similar?

Back

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

Front

What is the relationship between the segments created by a transversal intersecting two parallel lines?

Back

The segments are proportional to the lengths of the segments on the other side of the transversal.