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A parallelogram from two sides and a diagonal

Values

Construct a parallelogram ABCD with AB = 7 cm, BC = 4 cm and the diagonal AC = 8 cm.

Construct a parallelogram ABCD with AB = 6 cm, BC = 4 cm and the diagonal AC = 7 cm.

Construct a parallelogram ABCD with AB = 5 cm, BC = 3.5 cm and the diagonal AC = 6.5 cm.

Construct a parallelogram ABCD with AB = 6 cm, BC = 5 cm and the diagonal AC = 9 cm.

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1. Draw a base line and mark AB = 7 cm.

2. With A as the center and radius 8 cm, and B as the center and radius 4 cm, draw arcs that meet at C.

3. Join AC and BC: triangle ABC is half the parallelogram.

4. With A as the center and radius 4 cm, and C as the center and radius 7 cm, draw arcs that meet at D.

5. Join AD and CD: ABCD is the parallelogram.

1. Draw a base line and mark AB = 6 cm.

2. With A as the center and radius 7 cm, and B as the center and radius 4 cm, draw arcs that meet at C.

3. Join AC and BC: triangle ABC is half the parallelogram.

4. With A as the center and radius 4 cm, and C as the center and radius 6 cm, draw arcs that meet at D.

5. Join AD and CD: ABCD is the parallelogram.

1. Draw a base line and mark AB = 5 cm.

2. With A as the center and radius 6.5 cm, and B as the center and radius 3.5 cm, draw arcs that meet at C.

3. Join AC and BC: triangle ABC is half the parallelogram.

4. With A as the center and radius 3.5 cm, and C as the center and radius 5 cm, draw arcs that meet at D.

5. Join AD and CD: ABCD is the parallelogram.

1. Draw a base line and mark AB = 6 cm.

2. With A as the center and radius 9 cm, and B as the center and radius 5 cm, draw arcs that meet at C.

3. Join AC and BC: triangle ABC is half the parallelogram.

4. With A as the center and radius 5 cm, and C as the center and radius 6 cm, draw arcs that meet at D.

5. Join AD and CD: ABCD is the parallelogram.

Step 1 of 5
Why it works

A diagonal cuts a parallelogram into two congruent triangles. △ABC is drawn from its three sides, and △CDA from the same three (CD = AB, DA = BC, AC shared), turned round. Both pairs of opposite sides are then equal, so ABCD is a parallelogram.