Proving a quadrilateral is a parallelogram
- Turning the arrow around — 3 tasks
- The reason that assumes the conclusion — 3 tasks
- Same pair, or two different pairs — 3 tasks
- Proving the one-pair criterion — 3 tasks
- Going Deeper — 6 tasks
- Practice — 25 tasks
- Summary — 2 tasks
- Cool-down — 3 tasks
Classroom activities
Things a class does rather than writes on. Each one is a finished PDF: print it, cut it up if it says so, and hand it round.
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Must It Be a Parallelogram? — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 marked quadrilaterals (ticks, arrowheads, diagonals, printed lengths and angles), sorted into "must be a parallelogram", "cannot be one" and "cannot tell". The last row holds the near misses: one pair parallel with the other pair congruent, one pair of opposite angles, one diagonal cut in half. They are drawn to look like parallelograms on purpose.
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Which Fact Finishes the Proof? Proving Parallelograms — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page. Some ask which one more fact makes ABCD a parallelogram; others ask which reason proves it, or which reason uses it once it is proved. The wrong answers are the lesson's two big mistakes: the reason in the wrong direction, and a fact about the wrong pair (one pair parallel and the other pair congruent). The row of box numbers at the foot is the check.
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Do the Marks Make a Parallelogram? — Mystery Picture 25–35 minutes · 4 sheets
25 squares, each a quadrilateral drawn close to a parallelogram, with ticks, arrowheads, arcs, diagonals or printed numbers: fill the square only if the marks prove it is a parallelogram. Near misses (one pair parallel with the other pair congruent, one pair of opposite angles, one diagonal cut in half) and printed numbers that rule it out stay white. When every square is right, a picture appears.