Question

Converse Triangle Proportionality Theorem

A) If a line is parallel to one side of a triangle, it divides the other two sides proportionally.
B) If a line divides two sides of a triangle proportionally, it is parallel to the third side.
C) The sum of the angles of a triangle is always 180 degrees.
D) The length of the median of a triangle is half the length of the corresponding side.

Answer 1

The Converse Triangle Proportionality Theorem deals with a line dividing two sides of a triangle proportionally, indicating that this line is parallel to the third side. This geometry concept appears frequently in high school mathematics.

Step-by-step explanation:

The Converse Triangle Proportionality Theorem states that if a line divides two sides of a triangle proportionally, then it is parallel to the third side. This theorem is essentially the converse of the Triangle Proportionality Theorem, which states that if a line is parallel to one side of a triangle, it divides the other two sides proportionally.

For example, consider triangle ABC with sides AB, BC, and AC. If a line DE is drawn parallel to side BC, intersecting sides AB and AC at points D and E respectively, then according to the Triangle Proportionality Theorem, AD/DB = AE/EC. Conversely, if we know the proportions AD/DB = AE/EC hold for some line DE intersecting sides AB and AC, then according to the Converse Triangle Proportionality Theorem, the line DE must be parallel to side BC.