Questions: Which of the following is the Triangle Proportionality Theorem? A. A line parallel to one side of a triangle divides the other two sides proportionally. B. A line perpendicular to one side of a quadrilateral divides the other three sides proportionally. C. A line parallel to one side of a quadrilateral divides the other three sides proportionally. D. A line perpendicular to one side of a triangle divides the other two sides proportionally.

The answer is the first one (or A): A line parallel to one side of a triangle divides the other two sides proportionally.

Explanation for each option: A. A line parallel to one side of a triangle divides the other two sides proportionally.

• This is the correct statement of the Triangle Proportionality Theorem. It states that if a line is drawn parallel to one side of a triangle and intersects the other two sides, it divides those two sides into segments of proportional lengths.

B. A line perpendicular to one side of a quadrilateral divides the other three sides proportionally.

• This statement is incorrect. The Triangle Proportionality Theorem specifically applies to triangles, not quadrilaterals, and involves parallel lines, not perpendicular ones.

C. A line parallel to one side of a quadrilateral divides the other three sides proportionally.

• This statement is incorrect. The Triangle Proportionality Theorem does not apply to quadrilaterals, and it does not involve dividing three sides.

D. A line perpendicular to one side of a triangle divides the other two sides proportionally.

• This statement is incorrect. The Triangle Proportionality Theorem involves a line parallel to one side of a triangle, not perpendicular.

Summary: The correct answer is A: A line parallel to one side of a triangle divides the other two sides proportionally.