AHSME 1951 Problem 27

Through a point inside a triangle, three lines are drawn from the vertices to the opposite sides forming six triangular sections. Then: $\textbf{(A)}\ \text{the triangles are similar in opposite pairs} \textbf{(B)}\ \text{the triangles are congruent in opposite pairs}$ $\textbf{(C)}\ \text{the triangles are equal in area in opposite pairs} \textbf{(D)}\ \text{three similar quadrilaterals are formed}$ $\textbf{(E)}\ \text{none of the above relations are true}$