Problem: Through a point inside a triangle, three lines are drawn from the vertices to the opposite sides forming six triangular sections. Then:
Answer Choices:
A. The triangles are similar by opposite pairs.
B. The triangles are congruent by opposite pairs.
C. The triangles are equal in area by opposite pairs.
D. Three similar quadrilaterals are formed.
E. None of the above relations are true.
Solution:
We may eliminate (A) and (D) by proving that corresponding angles are not equal. If (A) is false, (B) is certainly false. We may eliminate (C) by placing the point very close to one side of the triangle. Thus none of the four statements is true.