A quadrilateral from five measures
Construct a quadrilateral ABCD with AB = 4.8 cm, BC = 4.3 cm, CD = 3.6 cm, DA = 4.2 cm and the diagonal AC = 6 cm.
Construct a quadrilateral ABCD with BC = 3.8 cm, AB = 4.5 cm, ∠ABC = 120°, ∠BCD = 105° and ∠BAD = 60°.
Construct a quadrilateral ABCD with BC = 5 cm, AB = 6 cm, CD = 5.7 cm, ∠ABC = 120° and ∠BCD = 105°.
Construct a quadrilateral ABCD with BC = 2.5 cm, AB = 3.5 cm, CD = 4 cm, ∠ABC = 75° and ∠BCD = 120°.
Construct a quadrilateral ABCD with AB = 3 cm, BC = 2.5 cm, AD = 3 cm and the diagonals AC = 4 cm and BD = 5 cm.
Construct a quadrilateral ABCD with AB = 3.6 cm, BC = 3.3 cm, AD = 2.7 cm and the diagonals AC = 4.6 cm and BD = 4 cm.
Construct a quadrilateral ABCD with AB = 3.8 cm, BC = 3.4 cm, CD = 4.5 cm, DA = 5 cm and ∠ABC = 60°.
1. Draw AB = 4.8 cm.
2. With A as the center and radius 6 cm, and B as the center and radius 4.3 cm, draw arcs that meet at C.
3. Join AC and BC.
4. With A as the center and radius 4.2 cm, and C as the center and radius 3.6 cm, draw arcs that meet at D.
5. Join AD and CD: ABCD is the quadrilateral.
1. Draw BC = 3.8 cm.
2. At B, construct ∠CBX = 120°, and with B as the center and radius 4.5 cm, cut BX at A.
3. At C, construct ∠BCY = 105°.
4. At A, construct ∠BAZ = 60°. AZ meets CY at D.
5. ABCD is the quadrilateral.
1. Draw BC = 5 cm.
2. At B, construct ∠CBX = 120°, and with B as the center and radius 6 cm, cut BX at A.
3. At C, construct ∠BCY = 105°, and with C as the center and radius 5.7 cm, cut CY at D.
4. Join AD: ABCD is the quadrilateral.
1. Draw BC = 2.5 cm.
2. At B, construct ∠CBX = 75°, and with B as the center and radius 3.5 cm, cut BX at A.
3. At C, construct ∠BCY = 120°, and with C as the center and radius 4 cm, cut CY at D.
4. Join AD: ABCD is the quadrilateral.
1. Draw AB = 3 cm.
2. With A as the center and radius 4 cm, and B as the center and radius 2.5 cm, draw arcs that meet at C.
3. Join AC and BC.
4. With A as the center and radius 3 cm, and B as the center and radius 5 cm, draw arcs that meet at D.
5. Join AD, CD and the diagonal BD: ABCD is the quadrilateral.
1. Draw AB = 3.6 cm.
2. With A as the center and radius 4.6 cm, and B as the center and radius 3.3 cm, draw arcs that meet at C.
3. Join AC and BC.
4. With A as the center and radius 2.7 cm, and B as the center and radius 4 cm, draw arcs that meet at D.
5. Join AD, CD and the diagonal BD: ABCD is the quadrilateral.
1. Draw AB = 3.8 cm.
2. At B, construct ∠ABX = 60°, and with B as the center and radius 3.4 cm, cut BX at C.
3. With A as the center and radius 5 cm, and C as the center and radius 4.5 cm, draw arcs that meet at D.
4. Join AD and CD: ABCD is the quadrilateral.
Why it works
A quadrilateral needs five measures, as a diagonal cuts it into two triangles and each needs three, with the diagonal shared. So it is built a triangle at a time: first the corners the given measures fix (a triangle from its sides, or a side and the angles at its ends), then the last corner where the last two measures meet.