A square
Construct a square ABCD with a side of 4 cm.
Construct a square ABCD with a side of 4.5 cm.
Construct a square ABCD with a side of 5 cm.
Construct a square ABCD with a side of 3.5 cm.
1. Draw a base line and mark AB = 4 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 square.
1. Draw a base line and mark AB = 4.5 cm.
2. At A, construct ∠BAX = 90° with a compass.
3. With A as the center and radius 4.5 cm, cut AX at D.
4. At B, construct ∠ABY = 90° with a compass.
5. With B as the center and radius 4.5 cm, cut BY at C.
6. Join CD: ABCD is the square.
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 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 square.
1. Draw a base line and mark AB = 3.5 cm.
2. At A, construct ∠BAX = 90° with a compass.
3. With A as the center and radius 3.5 cm, cut AX at D.
4. At B, construct ∠ABY = 90° with a compass.
5. With B as the center and radius 3.5 cm, cut BY at C.
6. Join CD: ABCD is the square.
Why it works
Both angles at the base are 90° and AD = BC = AB, so ABCD is a rectangle with all four sides equal: a square.