Which claims force the name
Show on a big screenA checks one measurement of a shape. A test can pass every parallelogram and still prove nothing.
- A rectangle. Its diagonals are ticked equal.
- It is a parallelogram. The test passes.
- An isosceles trapezium. Its diagonals are ticked equal too.
- It is not a parallelogram. The test still passed.
The rule
A parallelogram has both pairs of opposite sides parallel. Opposite sides do not share a corner.
Property — a fact that follows from the name. For example, a parallelogram has equal opposite sides. Test — a measurement that must earn the name. To earn the name is to prove the shape is a parallelogram.
Rule: A safe is passed by every parallelogram. No other shape passes it.
Equal diagonals fail the second half of the rule. The isosceles trapezium above passes the . Yet it is not a parallelogram. A trapezium has one pair of parallel sides. In an isosceles trapezium the other two sides, the legs, are equal.
| Test | Safe? | Why |
|---|---|---|
| Diagonals equal | No | An isosceles trapezium passes. A leaning parallelogram fails. |
| One pair of opposite sides equal | No | A trapezium with equal legs passes. |
| Both pairs of opposite sides equal | Yes | Only parallelograms pass. |
| Diagonals bisect each other | Yes | Only parallelograms pass. |
One equal pair is not enough to earn the name. Sides 6, 3, 6, 4, in that order, give one matching pair. That shape is not a parallelogram.
The next lessons prove the safe one at a time.
Tap Next . Watch which shapes fool it.
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Try the lab to finish this lesson.