Three four-sided figures

The figure shows quadrilateral A B C D. A B and D C each carry one arrowhead, and there are no other marks on the figure. What kind of quadrilateral is A B C D? Compare these three marked shapes. Start with this one arrowhead. The side opposite carries the matching arrowhead. Matching arrowheads mark parallel sides. Two arrowheads on each of the other sides mark a second parallel pair. A parallelogram has two pairs of parallel sides. The rhombus also has two pairs of parallel sides. Its four matching ticks tell us that all four sides are equal in length. A rhombus is a parallelogram with all four sides equal. The trapezium has exactly one pair of parallel sides. Arrowheads show parallel sides. Ticks show equal lengths. Now read the marks on the question figure. A B carries one arrowhead. D C carries the matching arrowhead. So A B is parallel to D C. A D has no arrowhead. B C has no arrowhead either. A parallelogram would need a second pair of parallel sides. This figure has one pair only, so A B C D is a trapezium.

Your turn, on a new figure. The figure shows parallelogram A B C D. A B is nine centimetres and B C is five centimetres. Find the length of D C. Try it first. Pause if you like. Start with the side D C. A B and D C carry the same mark. A B is opposite D C, across the figure. The question tells us this is a parallelogram. Its opposite sides are equal in length. So D C equals A B, which is nine centimetres. A D and B C carry two arrowheads. That is the other pair. Read the marks, then use the property of the given shape.