Geometry and proof · Ages 14–15

Properties of a parallelogram worksheet

Part of: Quadrilaterals

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Geometry and proof · Ages 14–15

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.ABCD is a parallelogram. x =
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2.ABCD is a parallelogram. x =
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3.ABCD is a parallelogram whose diagonals cross at E, with AE = 3 cm and BE = 2 cm. x = , BD = cm
Fill in each blank
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4.ABCD is a parallelogram. x =
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5.In the parallelogram ABCD, ∠A = (x + 48)° and ∠C = (6x − 27)°. x =
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6.In the parallelogram ABCD, ∠A = (2x + 63)° and ∠C = (5x − 24)°. x =
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7.ABCD is a parallelogram whose diagonals cross at E, with AE = 5 cm and BE = 6 cm. x = , BD = cm
Fill in each blank
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8.In the parallelogram ABCD, ∠A = (x + 53)° and ∠C = (3x − 5)°. x =
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9.ABCD is a parallelogram whose diagonals cross at E, with AE = 5 cm and BE = 3 cm. x = , BD = cm
Fill in each blank
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10.The parallelogram ABCD has a perimeter of 36 cm, and AB is 4 cm longer than BC. AB =
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11.The parallelogram ABCD has a perimeter of 18 cm, and AB is 3 cm longer than BC. AB =
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13.A flower bed shaped as a parallelogram has a perimeter of 184 m, its long sides 12 m longer than its short ones. How long is a long side?
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14.A floor tile is a parallelogram, one of its angles 85°. With ∠A = 85°, the other three are ∠B = °, ∠C = ° and ∠D = °.
Fill in each blank
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15.Each cell of a folding gate is a parallelogram, its two diagonal bars bolted together at E. AE = 47 cm and BE = 35 cm. The diagonal AC = cm and BD = cm.
Fill in each blank
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16.A field ABCD is a parallelogram with AB = 30 m and BC = 13 m. CD = m, AD = m, and the fence round it is m long.
Fill in each blank
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17.Each cell of a folding gate is a parallelogram, its two diagonal bars bolted together at E. AE = 62 cm and BE = 58 cm. The diagonal AC = cm and BD = cm.
Fill in each blank
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18.A flower bed shaped as a parallelogram has a perimeter of 208 m, its long sides 8 m longer than its short ones. How long is a long side?
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Show the answers and working

Properties of a parallelogram worksheet: Answers and working

1. 80°
∠C and ∠A are opposite: x = 80° (opp. ∠s of // gram).
2. 9 cm
DC and AB are opposite sides: x = 9 (opp. sides of // gram).
3. 3, 4
The diagonals bisect each other (diags. of // gram): x = AE = 3, BD = 2 × 2 = 4 cm.
4. 110°
AD // BC, so ∠A and ∠B are interior angles: x = 180° − 70° = 110°.
5. 15
Opposite angles are equal: x + 48 = 6x − 27, so x = 15. Check: both angles are 63°.
6. 29
Opposite angles are equal: 2x + 63 = 5x − 24, so x = 29. Check: both angles are 121°.
7. 5, 12
The diagonals bisect each other (diags. of // gram): x = AE = 5, BD = 2 × 6 = 12 cm.
8. 29
Opposite angles are equal: x + 53 = 3x − 5, so x = 29. Check: both angles are 82°.
9. 5, 6
The diagonals bisect each other (diags. of // gram): x = AE = 5, BD = 2 × 3 = 6 cm.
10. 11 cm
Opposite sides are equal, so AB + BC = 36 ÷ 2; AB = (that + 4) ÷ 2 = 11 cm.
11. 6 cm
Opposite sides are equal, so AB + BC = 18 ÷ 2; AB = (that + 3) ÷ 2 = 6 cm.

12. B. the diagonals are equal
Equal diagonals belong to rectangles; a general parallelogram's diagonals differ in length.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 52 m
Long + short = 184 ÷ 2; long = (that + 12) ÷ 2 = 52 m.
14. 95, 85, 95
∠B = 180° − 85° = 95° (int. ∠s); ∠C = ∠A = 85° and ∠D = ∠B = 95° (opp. ∠s of // gram).
15. 94, 70
A parallelogram's diagonals bisect each other: AC = 2 × 47 = 94 cm and BD = 2 × 35 = 70 cm.
16. 30, 13, 86
Opposite sides of a parallelogram are equal: CD = AB = 30 m and AD = BC = 13 m; perimeter = 2 × (30 + 13) = 86 m.
17. 124, 116
A parallelogram's diagonals bisect each other: AC = 2 × 62 = 124 cm and BD = 2 × 58 = 116 cm.
18. 56 m
Long + short = 208 ÷ 2; long = (that + 8) ÷ 2 = 56 m.

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