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Problems Geometry Plane geometry Area Area of a trapezium

In a trapezium $A B C D$ , the side $A B$ is parallel to the side $C D$ . Show that the areas of triangles $△ A B C$ and $△ A B D$ are equal.

Problem #PRU-34905

Problems Geometry Plane geometry Area Area of a trapezium Area ratio Area ratio (other) Methods Pigeonhole principle Pigeonhole principle (finite number of poits, lines etc.) Quadrilateral Parallelogram Special cases Rectangles and squares. Criteria and properties

13–14 4.0

9 straight lines each divide a square into two quadrilaterals, with their areas having a ratio of $2 : 3$ . Prove that at least three of the nine lines pass through the same point.