A rhombus
Construct a rhombus ABCD with diagonals AC = 8.6 cm and BD = 6.2 cm.
Construct a rhombus ABCD with diagonals AC = 6.6 cm and BD = 4.8 cm.
Construct a rhombus ABCD with side AB = 5.3 cm and ∠ABC = 45°.
Construct a rhombus ABCD with side AB = 5.1 cm and ∠ABC = 105°.
Construct a rhombus ABCD with side AB = 5.5 cm and diagonal AC = 7 cm.
Construct a rhombus ABCD with side AB = 5.1 cm and diagonal AC = 8.2 cm.
Construct a rhombus ABCD with side AB = 4.7 cm and ∠CAB = 60°.
Construct a rhombus ABCD with side AB = 5.3 cm and ∠CAB = 30°.
1. Draw the diagonal AC = 8.6 cm.
2. Draw the perpendicular bisector of AC. It cuts AC at O.
3. With O as the center and radius 3.1 cm (half of BD), cut the bisector on both sides of AC at B and D.
4. Join AB, BC, CD and DA: ABCD is the rhombus.
1. Draw the diagonal AC = 6.6 cm.
2. Draw the perpendicular bisector of AC. It cuts AC at O.
3. With O as the center and radius 2.4 cm (half of BD), cut the bisector on both sides of AC at B and D.
4. Join AB, BC, CD and DA: ABCD is the rhombus.
1. Draw AB = 5.3 cm.
2. At B, construct ∠ABX = 45°, and with B as the center and radius 5.3 cm, cut BX at C.
3. With A and C as the centers and radius 5.3 cm, draw arcs that meet at D.
4. Join AD and CD: ABCD is the rhombus.
1. Draw AB = 5.1 cm.
2. At B, construct ∠ABX = 105°, and with B as the center and radius 5.1 cm, cut BX at C.
3. With A and C as the centers and radius 5.1 cm, draw arcs that meet at D.
4. Join AD and CD: ABCD is the rhombus.
1. Draw the diagonal AC = 7 cm.
2. Draw the perpendicular bisector of AC. It cuts AC at O.
3. With A as the center and radius 5.5 cm, cut the bisector on both sides of AC at B and D.
4. Join AB, BC, CD and DA: ABCD is the rhombus.
1. Draw the diagonal AC = 8.2 cm.
2. Draw the perpendicular bisector of AC. It cuts AC at O.
3. With A as the center and radius 5.1 cm, cut the bisector on both sides of AC at B and D.
4. Join AB, BC, CD and DA: ABCD is the rhombus.
1. Draw AB = 4.7 cm.
2. At A, construct ∠BAX = 60°.
3. With B as the center and radius AB = 4.7 cm, cut AX at C. Join BC.
4. With A and C as the centers and radius 4.7 cm, draw arcs that meet at D.
5. Join AD and CD: ABCD is the rhombus.
1. Draw AB = 5.3 cm.
2. At A, construct ∠BAX = 30°.
3. With B as the center and radius AB = 5.3 cm, cut AX at C. Join BC.
4. With A and C as the centers and radius 5.3 cm, draw arcs that meet at D.
5. Join AD and CD: ABCD is the rhombus.
Why it works
All four sides of a rhombus are equal, and its diagonals bisect each other at right angles. So from the diagonals, B and D are on the perpendicular bisector of AC, half of BD from the middle; from a side and a diagonal, they are on it a side’s length from A. From a side and an angle, the last corner is a side’s length from two corners already drawn.