KA-0079Properties of triangles and quadrilaterals
3 points, difficulty 1 of 3Level 3–4about 60sWhich of these is true of every rectangle?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Test each claim on a long thin rectangle.
2The strategy
A claim about every rectangle has to hold for a very long thin one as well as for a square. Draw a 1 by 8 rectangle and check each statement against it.
3The full solution
On a long thin rectangle the sides are not all equal, the diagonals meet at a shallow angle, and there are only two lines of symmetry. But the two diagonals are still the same length.
Solution— no shortcut on this one
Test each claim against an extreme example — a 1 by 8 rectangle. Its sides are not all equal, so A fails. Its diagonals cross at a shallow angle, so B fails. It has only two lines of symmetry, the two midlines, so C fails. Any quadrilateral's angles add to 360, not 180, so D fails. Its two diagonals are both the same length, and that is true of every rectangle. The transferable idea: to test always, try the least typical example you can draw.
Why this is on the test: Named shapes carry guaranteed facts and tempting extra ones, and a square is the example that makes every false claim look true.