A trapezium
Construct a trapezium ABCD with AB ∥ DC, AB = 8 cm, BC = 6 cm, CD = 4 cm and ∠ABC = 60°.
Construct a trapezium ABCD with AB ∥ DC, AB = 6 cm, BC = 4 cm, CD = 3.2 cm and ∠ABC = 75°.
Construct a trapezium ABCD with AB ∥ DC, AB = 7 cm, BC = 4 cm, CD = 4 cm and DA = 5 cm.
Construct a trapezium ABCD with AB ∥ DC, AB = 10 cm, BC = 4 cm, CD = 6 cm and DA = 3 cm.
Construct a trapezium ABCD with AB ∥ DC, AB = 10 cm, BC = 5 cm, CD = 6 cm and the diagonal AC = 8 cm.
Construct a trapezium ABCD with AB ∥ DC, AB = 7 cm, BC = 6 cm, ∠BAD = 90° and ∠ABC = 75°.
1. Draw AB = 8 cm.
2. At B, construct ∠ABX = 60°, and with B as the center and radius 6 cm, cut BX at C.
3. At C, construct ∠BCY = 180° − 60° = 120°: then CY ∥ AB.
4. With C as the center and radius 4 cm, cut CY at D. Join AD.
5. ABCD is the trapezium, with AB ∥ DC.
1. Draw AB = 6 cm.
2. At B, construct ∠ABX = 75°, and with B as the center and radius 4 cm, cut BX at C.
3. At C, construct ∠BCY = 180° − 75° = 105°: then CY ∥ AB.
4. With C as the center and radius 3.2 cm, cut CY at D. Join AD.
5. ABCD is the trapezium, with AB ∥ DC.
1. Draw AB = 7 cm.
2. With A as the center and radius DC = 4 cm, cut AB at E.
3. With E as the center and radius AD = 5 cm, and B as the center and radius 4 cm, draw arcs that meet at C. Join BC (and EC, a help line).
4. With C as the center and radius 4 cm, and A as the center and radius 5 cm, draw arcs that meet at D. Join CD and DA.
5. ABCD is the trapezium, with AB ∥ DC.
1. Draw AB = 10 cm.
2. With A as the center and radius DC = 6 cm, cut AB at E.
3. With E as the center and radius AD = 3 cm, and B as the center and radius 4 cm, draw arcs that meet at C. Join BC (and EC, a help line).
4. With C as the center and radius 6 cm, and A as the center and radius 3 cm, draw arcs that meet at D. Join CD and DA.
5. ABCD is the trapezium, with AB ∥ DC.
1. Draw AB = 10 cm.
2. With A as the center and radius 8 cm, and B as the center and radius 5 cm, draw arcs that meet at C. Join AC and BC.
3. At C, copy ∠BAC on the other side of AC, as ∠ACY: alternate angles, so CY ∥ AB.
4. With C as the center and radius 6 cm, cut CY at D. Join AD.
5. ABCD is the trapezium, with AB ∥ DC.
1. Draw AB = 7 cm.
2. At A, construct ∠BAX = 90°.
3. At B, construct ∠ABX = 75°, and with B as the center and radius 6 cm, cut BX at C.
4. At C, construct ∠BCY = 180° − 75° = 105°: then CY ∥ AB.
5. CY meets AX at D.
6. ABCD is the trapezium, with AB ∥ DC.
Why it works
DC has to be parallel to AB. An angle at C that makes the two angles on the same side of BC add up to 180° (co-interior angles), or that copies ∠BAC on the other side of AC (alternate angles), gives that parallel line. With four sides, AECD is a parallelogram (AE = DC, EC = AD), so EBC is a triangle with sides AB − DC, BC and AD.