Question

Which of the following is not part of the Triangle Proportionality Theorem?

O
A. AA Similarity Theorem
O
B. Two sides divided proportionally.
O
C. A parallel line to one side of a triangle.
O
D. A perpendicular line to one side of a triangle.

Answer 1

C. A parallel line to one side of a triangle.

* I was so scared if that's not the correct answer.

But it sure was the answer.

Don't hesitate!

Answer 2

A. AA Similarity Theorem . True

B. Two sides divided proportionally. True

C. A parallel line to one side of a triangle. True

D. A perpendicular line to one side of a triangle. False

Explanation:

The Triangle Proportionality Theorem says that if a line is parallel to one side of a triangle, then it splits the other two sides into proportional sections.

Now, here the given statements are:

A. AA Similarity Theorem

TRUE, as the angles opposite to equal sides are equal.

And if lines are divided proportionally, both the triangles are Similar by AA similarity theorem.

B. Two sides divided proportionally.

TRUE,as the other two sides of the triangle are divided proportionally by the parallel line.

C. A parallel line to one side of a triangle.

TRUE, as the parallel line divides the other two non- parallel sides in equal proportions.

D. A perpendicular line to one side of a triangle.

FALSE, this part is not required anywhere in the given theorem result.