Building one from measurements
A surveyor measures land and does not guess a field's shape. Are four side lengths enough to build that shape?
Watch out!
Ask an adult before you use a new compass. A fresh point is sharper than it looks.
- Draw the first side, 6 long.
- Arcs of 8 and 5 from its ends cross at the third corner.
- Arcs of 6 and 5 cross at the fourth corner.
- Join the four corners: the quadrilateral is built.
No. Four sides can make more than one shape. A compass draws an arc, which is part of a circle.
Rule: Four sides alone can close in more than one shape. A fifth measurement, a diagonal, decides the shape. Draw the diagonal inside the shape. The other two corners are then on opposite sides of the diagonal.
Sides of 7, 4, 5, 6 close with a diagonal of 8. The same four sides also close with a diagonal of 6. Same sides, two different shapes.
Some sets of measurements do not close at all. Sides 6, 2, 5, 5 with a diagonal of 9 fail. The arc of 2 starts at the second corner. It reaches at most 6 + 2 = 8 from the first corner. So it cannot reach 9.
Drag the slider to pick a diagonal. See if the shape closes.
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