Properties of Parallelograms Worksheet
Explore and apply the properties of parallelograms including sides, angles, and diagonals at a Grade 11 level with this comprehensive worksheet.
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Properties of Parallelograms
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. Which of the following statements is NOT always true for a parallelogram?
Opposite sides are congruent.
Opposite angles are congruent.
Diagonals are congruent.
Consecutive angles are supplementary.
2. In parallelogram ABCD, if m∠A = (3x + 10)° and m∠C = (5x - 20)°, what is the value of x?
5
10
15
20
3. In a parallelogram, opposite sides are and .
4. The diagonals of a parallelogram each other.
5. Consider parallelogram PQRS. If PQ = 7 cm, QR = 5 cm, and m∠P = 110°, find the lengths of RS and SP, and the measures of ∠Q, ∠R, and ∠S.
RS =
SP =
m∠Q =
m∠R =
m∠S =
6. The diagonals of parallelogram EFGH intersect at point I. If EI = 3x - 4 and IG = x + 6, find the length of EG.
7. All rectangles are parallelograms.
True
False
8. All rhombuses are parallelograms.
True
False
9. The perimeter of a parallelogram is 60 cm. If one side is 10 cm longer than the other side, find the lengths of all sides of the parallelogram.
10. In parallelogram JKLM, the coordinates of the vertices are J(0,0), K(5,0), L(7,3), and M(2,3). Verify that the diagonals bisect each other by finding the midpoints of JL and KM.