A rectangle
Construct a rectangle ABCD with AB = 5 cm and AD = 3 cm.
Construct a rectangle ABCD with AB = 7 cm and AD = 4 cm.
Construct a rectangle ABCD with AB = 6 cm and AD = 4 cm.
Construct a rectangle ABCD with AB = 8 cm and AD = 5 cm.
1. Draw a base line and mark AB = 5 cm.
2. At A, construct ∠BAX = 90° with a compass.
3. With A as the center and radius 3 cm, cut AX at D.
4. At B, construct ∠ABY = 90° with a compass.
5. With B as the center and radius 3 cm, cut BY at C.
6. Join CD: ABCD is the rectangle.
1. Draw a base line and mark AB = 7 cm.
2. At A, construct ∠BAX = 90° with a compass.
3. With A as the center and radius 4 cm, cut AX at D.
4. At B, construct ∠ABY = 90° with a compass.
5. With B as the center and radius 4 cm, cut BY at C.
6. Join CD: ABCD is the rectangle.
1. Draw a base line and mark AB = 6 cm.
2. At A, construct ∠BAX = 90° with a compass.
3. With A as the center and radius 4 cm, cut AX at D.
4. At B, construct ∠ABY = 90° with a compass.
5. With B as the center and radius 4 cm, cut BY at C.
6. Join CD: ABCD is the rectangle.
1. Draw a base line and mark AB = 8 cm.
2. At A, construct ∠BAX = 90° with a compass.
3. With A as the center and radius 5 cm, cut AX at D.
4. At B, construct ∠ABY = 90° with a compass.
5. With B as the center and radius 5 cm, cut BY at C.
6. Join CD: ABCD is the rectangle.
Why it works
Both angles at the base are 90°, so AD and BC are perpendicular to AB, and so parallel to each other; they are also equal. A quadrilateral with a pair of equal, parallel sides is a parallelogram, and one with a right angle is a rectangle.