240. Parallel Pairs & Slides · parallelogram vs trapezium definitions
ABCD is a parallelogram when both pairs of opposite sides are parallel. Drag D to break the second pair and see it become a trapezium.
What this lesson covers
Try to break it
Drag C and D along the top line. The top side CD slides, but it stays parallel to AB throughout — that's what the constraint enforces. The parallelogram shears (AD and BC tilt) but the two pairs of opposite sides never lose their parallelism.
How you build it
Construct a trapezium with one pair of parallel sides.
- Point tool: mark point A at the bottom-left.
- Point tool: mark point B to the right of A.
- Segment tool: join A to B — this is the parallel side that stays put.
- Point tool: mark point D above A — the top-left corner.
- Parallel tool: click D, then click on AB. The line through D is exactly parallel to AB — that fixes the one parallel pair.
- Point tool: mark point C on the parallel line, away from D, so DC is a different length from AB — making it a trapezium, not a parallelogram.
- Segment tool: join D to A.
- Segment tool: join B to C. AB ∥ DC but AD and BC are not parallel — a trapezium.
The proof, step by step
Prove that ABCD is a parallelogram — both pairs of opposite sides parallel.
- A parallelogram is defined by two pairs of parallel opposite sides.
- A trapezium is defined by exactly one pair of parallel opposite sides.
- Dragging D horizontally breaks the parallelism of AD and BC while keeping AB and CD parallel.
Worked example
A quadrilateral has one pair of parallel opposite sides and one pair of non-parallel opposite sides. What is it called?
By definition, a quadrilateral with exactly one pair of parallel opposite sides is a trapezium. A parallelogram requires two pairs.
- Parallelogram
- Rectangle
- Trapezium — correct
- Rhombus