A parallelogram from two sides and an angle
Construct a parallelogram ABCD with AB = 7 cm, AD = 4 cm and ∠DAB = 60°.
Construct a parallelogram ABCD with AB = 5 cm, AD = 3 cm and ∠DAB = 45°.
Construct a parallelogram ABCD with AB = 6 cm, AD = 4 cm and ∠DAB = 75°.
Construct a parallelogram ABCD with AB = 5 cm, AD = 4 cm and ∠DAB = 120°.
1. Draw a base line and mark AB = 7 cm.
2. At A, construct ∠BAX = 60° with a compass.
3. With A as the center and radius 4 cm, cut AX at D.
4. With B as the center and radius AD = 4 cm, draw an arc above B. With D as the center and radius AB = 7 cm, cut it at C.
5. Join BC and DC: ABCD is the parallelogram.
1. Draw a base line and mark AB = 5 cm.
2. At A, construct ∠BAX = 45° with a compass.
3. With A as the center and radius 3 cm, cut AX at D.
4. With B as the center and radius AD = 3 cm, draw an arc above B. With D as the center and radius AB = 5 cm, cut it at C.
5. Join BC and DC: ABCD is the parallelogram.
1. Draw a base line and mark AB = 6 cm.
2. At A, construct ∠BAX = 75° with a compass.
3. With A as the center and radius 4 cm, cut AX at D.
4. With B as the center and radius AD = 4 cm, draw an arc above B. With D as the center and radius AB = 6 cm, cut it at C.
5. Join BC and DC: ABCD is the parallelogram.
1. Draw a base line and mark AB = 5 cm.
2. At A, construct ∠BAX = 120° with a compass.
3. With A as the center and radius 4 cm, cut AX at D.
4. With B as the center and radius AD = 4 cm, draw an arc above B. With D as the center and radius AB = 5 cm, cut it at C.
5. Join BC and DC: ABCD is the parallelogram.
Why it works
C is AD from B and AB from D, so both pairs of opposite sides are equal. A quadrilateral whose opposite sides are equal is a parallelogram, and its angle at A is the one constructed.