Question

question 1 of 10
which of the following is the triangle proportionality theorem?
a. a line perpendicular 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 triangle divides the other two sides proportionally.
d. a line parallel to one side of a quadrilateral divides the other three sides proportionally.

Explanation:

The Triangle Proportionality Theorem (also known as Thales' theorem) specifically pertains to triangles. It states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

• Option A: Incorrect as the line should be parallel, not perpendicular.
• Option B: Incorrect as the theorem is about triangles, not quadrilaterals.
• Option C: Correct as it matches the statement of the Triangle Proportionality Theorem.
• Option D: Incorrect as it refers to a quadrilateral, which is not the subject of the theorem.

Answer:

C. A line parallel to one side of a triangle divides the other two sides proportionally.