Which claims force the name
A test 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 test 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 test. 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 tests one at a time.
Tap Next test. Watch which shapes fool it.
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