A parallelogram equal to a parallelogram
Construct parallelogram ABCD with AB = 4 cm, BC = 5.5 cm and ∠ABC = 60°. Then construct a parallelogram ABQP of the same area with ∠ABQ = 120°.
Construct parallelogram ABCD with AB = 4 cm, BC = 5.5 cm and ∠ABC = 60°. Then construct a parallelogram ABQP of the same area with AP = 6 cm.
Construct parallelogram ABCD with AB = 5 cm, BC = 4 cm and ∠ABC = 60°. Then construct a parallelogram ABQP of the same area with ∠ABQ = 90° (a rectangle).
Construct parallelogram ABCD with AB = 4.5 cm, BC = 4.8 cm and ∠ABC = 75°. Then construct a parallelogram ABQP of the same area with AP = 5.5 cm.
Construct parallelogram ABCD with AB = 5 cm, BC = 4 cm and ∠ABC = 120°. Then construct a parallelogram ABQP of the same area with ∠ABQ = 75°.
1. Draw AB = 4 cm.
2. At B, construct ∠ABC = 60° and cut BC = 5.5 cm on its arm.
3. With A as the center and radius 5.5 cm, and C as the center and radius 4 cm, draw arcs that cut at D. Join AD and CD: ABCD is the given parallelogram.
4. Produce DC both ways to make the line ST.
5. At B, construct ∠ABQ = 120°; its arm meets ST at Q.
6. With Q as the center and radius AB = 4 cm, cut QS at P. Join AP: ABQP is the parallelogram.
1. Draw AB = 4 cm.
2. At B, construct ∠ABC = 60° and cut BC = 5.5 cm on its arm.
3. With A as the center and radius 5.5 cm, and C as the center and radius 4 cm, draw arcs that cut at D. Join AD and CD: ABCD is the given parallelogram.
4. Produce DC both ways to make the line ST.
5. With A as the center and radius 6 cm, cut ST at P.
6. With P as the center and radius AB = 4 cm, cut PT at Q. Join AP and BQ: ABQP is the parallelogram.
1. Draw AB = 5 cm.
2. At B, construct ∠ABC = 60° and cut BC = 4 cm on its arm.
3. With A as the center and radius 4 cm, and C as the center and radius 5 cm, draw arcs that cut at D. Join AD and CD: ABCD is the given parallelogram.
4. Produce DC both ways to make the line ST.
5. At B, construct ∠ABQ = 90°; its arm meets ST at Q.
6. With Q as the center and radius AB = 5 cm, cut QS at P. Join AP: ABQP is the parallelogram.
1. Draw AB = 4.5 cm.
2. At B, construct ∠ABC = 75° and cut BC = 4.8 cm on its arm.
3. With A as the center and radius 4.8 cm, and C as the center and radius 4.5 cm, draw arcs that cut at D. Join AD and CD: ABCD is the given parallelogram.
4. Produce DC both ways to make the line ST.
5. With A as the center and radius 5.5 cm, cut ST at P.
6. With P as the center and radius AB = 4.5 cm, cut PT at Q. Join AP and BQ: ABQP is the parallelogram.
1. Draw AB = 5 cm.
2. At B, construct ∠ABC = 120° and cut BC = 4 cm on its arm.
3. With A as the center and radius 4 cm, and C as the center and radius 5 cm, draw arcs that cut at D. Join AD and CD: ABCD is the given parallelogram.
4. Produce DC both ways to make the line ST.
5. At B, construct ∠ABQ = 75°; its arm meets ST at Q.
6. With Q as the center and radius AB = 5 cm, cut QS at P. Join AP: ABQP is the parallelogram.
Why it works
ABCD and ABQP stand on the same base AB, and their tops DC and PQ lie on one line ST ∥ AB, so they have the same height. Parallelograms on the same base and between the same parallels are equal in area.