Skills · Geometry · Polygons & Quadrilaterals

Properties of parallelograms

Printable practice with an answer key the engine computes, at three levels, in as many versions as you need.

Problem types

Sample Sheet · Level 1

  1. parallelogram ABCD: AD ?, BC 27, AB 29ABCD?2729
    ABCD is a parallelogram. Find the length marked ?.
  2. parallelogram ABCD: ∠B ?, ∠D 72°ABCD?72°
    ABCD is a parallelogram. Find the measure of the angle marked ?.
  3. parallelogram ABCD, diagonals meeting at E: AE ?, AC 32, BE 18ABCDE?18
    ABCD is a parallelogram. AC = 32. Find the length marked ?.
  4. parallelogram ABCD: ∠A 59°, ∠B ?ABCD59°?
    ABCD is a parallelogram. Find the measure of the angle marked ?.
  5. parallelogram ABCD, diagonals meeting at E: AE ?, AC 28, BE 17ABCDE?17
    ABCD is a parallelogram. AC = 28. Find the length marked ?.
  6. parallelogram ABCD: ∠A ?, ∠C 54°ABCD?54°
    ABCD is a parallelogram. Find the measure of the angle marked ?.
  7. parallelogram ABCD: AD 9, BC ?, AB 22ABCD9?22
    ABCD is a parallelogram. Find the length marked ?.
  8. parallelogram ABCD: ∠B ?, ∠C 110°ABCD?110°
    ABCD is a parallelogram. Find the measure of the angle marked ?.

Answer key

  1. 27 units
  2. 72°
  3. 16 units
  4. 121°
  5. 14 units
  6. 54°
  7. 9 units
  8. 70°

Sample Sheet · Level 3

  1. parallelogram ABCD: ∠B (x + 49)°, ∠D (4x − 29)°ABCD(x + 49)°(4x − 29)°
    ABCD is a parallelogram. Find m∠D.
  2. parallelogram ABCD: AD 5x − 29, BC x + 15, AB 3x − 9ABCD5x − 29x + 153x − 9
    ABCD is a parallelogram. Find AD.
  3. parallelogram ABCD: ∠B (6x − 34)°, ∠C (2x − 2)°ABCD(6x − 34)°(2x − 2)°
    ABCD is a parallelogram. Find m∠C.
  4. parallelogram ABCD: ∠D (x + 36)°, ∠A (3x + 24)°ABCD(x + 36)°(3x + 24)°
    ABCD is a parallelogram. Find m∠A.
  5. parallelogram ABCD, diagonals meeting at E: BE 6x + 4, BD 5x + 22, AE 10ABCDE6x + 410
    ABCD is a parallelogram. BD = 5x + 22. Find BD.
  6. parallelogram ABCD: ∠A (3x − 25)°, ∠C (x + 29)°ABCD(3x − 25)°(x + 29)°
    ABCD is a parallelogram. Find m∠C.
  7. parallelogram ABCD, diagonals meeting at E: BE x + 15, ED 3x − 21, AE 20ABCDEx + 153x − 2120
    ABCD is a parallelogram. Find BE.
  8. parallelogram ABCD: AB 3x − 26, DC x + 4, BC 2x − 6ABCD3x − 26x + 42x − 6
    ABCD is a parallelogram. Find DC.

Answer key

  1. 75°
  2. 26 units
  3. 52°
  4. 114°
  5. 32 units
  6. 56°
  7. 33 units
  8. 19 units

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