Properties of parallelograms: sides, angles, diagonals
- Four claims against one picture — 3 tasks
- Rubbing out two sides to find the Z — 3 tasks
- One diagonal, two congruent triangles — 3 tasks
- Where the diagonals cross — 3 tasks
- What the diagonal result does not say — 4 tasks
- Practice — 23 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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Same Number, 180° Minus, or Can You Not Tell? Parallelograms — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 lettered parallelograms, each with a part and its number and another part with a question mark. Students do not work anything out: they decide whether the question mark is the same number, 180° minus it, or cannot be told. The last row holds what the properties do not say: a piece of the other diagonal, two sides next to each other, a corner cut by a diagonal, and two angles on one side of a diagonal.
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Across, Next Door, or Only Half? Parallelograms — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page, each with its own small parallelogram PQRS. Half the boxes are about two angles, across from each other or next to each other, with numbers or with x; half are about the diagonals, a piece or the whole. The wrong answers are the two costliest mistakes on this topic: swapping "equal" and "add to 180°", and taking a piece of a diagonal (or x) for the length asked. The row of box numbers at the foot is the check.
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Must These Two Angles Be Equal? Parallelograms — Mystery Picture 25–35 minutes · 4 sheets
25 parallelograms, each with two angles marked: fill the square if the two angles must be equal in every parallelogram, leave it white if not. The white squares are the pairs students really mix up: corners next to each other, the two parts of a corner cut by a diagonal, angles on one side of a diagonal, and angles side by side where the diagonals cross. Some are drawn close to a rectangle or a rhombus, so the eye alone is not enough. When every square is right, a picture appears.
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Across or Next Door? Half or Whole? Parallelograms — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each one slanted parallelogram. Half the cards give a corner angle and ask for the angle across from it or next to it; half give pieces of the diagonals and ask for a whole diagonal or a piece. Mixing up "across" and "next to", or pairing a piece of one diagonal with a piece of the other, lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.