Parallelograms Special Quadrilaterals Worksheet with Answers – Geometry (Free PDF)

Problem 1 Opposite sides of a parallelogram ★★★

In parallelogram ABCD, AB = 14.5 and BC = 9. Find CD, AD and the perimeter.

Problem 2 Angles of a parallelogram ★★★

In parallelogram ABCD, m∠A = 68°. Find the other three angles.

Problem 3 Diagonals that bisect ★★★

The diagonals of parallelogram ABCD meet at E. AE = 6.5 and BE = 9.25. Find CE, DE, AC and BD.

Problem 4 Opposite sides with algebra ★★★

In parallelogram ABCD, AB = 4x − 7 and CD = 2x + 9. Find x and AB.

Problem 5 Consecutive angles with algebra ★★★

In parallelogram ABCD, m∠A = (4x + 6)° and m∠B = (6x − 16)°. Find x and both angles.

Problem 6 Diagonals with algebra ★★★

The diagonals of parallelogram ABCD meet at E. AE = 3x + 1 and EC = 5x − 9. Find x and AC.

Problem 7 Is it a parallelogram ★★★

Decide whether each description guarantees a parallelogram. Name the test or give a reason it fails.

1. Opposite sides measure 9 and 9, and 14 and 14.
2. Opposite angles measure 70° and 70°, and 110° and 110°.
3. One pair of opposite sides is parallel and the other pair is congruent.
4. The diagonals bisect each other.

Problem 8 Make it a parallelogram ★★★

In quadrilateral ABCD, AB = 2x + 5, CD = 4x − 9, AD = 3y − 1 and BC = y + 7. Find x and y so that ABCD is a parallelogram.

Problem 9 Parallelogram on the plane ★★★

The vertices of quadrilateral ABCD are A(1, 2), B(6, 3), C(8, 7) and D(3, 6). Use the midpoints of the diagonals to decide whether it is a parallelogram.

Problem 10 Rectangle diagonals ★★★

The diagonals of rectangle ABCD measure AC = 5x − 3 and BD = 3x + 11. Find x and the length of each diagonal.

Problem 11 Diagonal of a rhombus ★★★

A rhombus has a perimeter of 52 and one diagonal of 10. Find the side length, the other diagonal and the area.

Problem 12 Angles of a rhombus ★★★

In rhombus ABCD, m∠DAB = 64°. Find m∠ABC, m∠CAB and m∠ABD.

Problem 13 Trapezoid midsegment ★★★

The midsegment of a trapezoid measures (3x + 11), and the bases measure (4x + 2) and (6x − 8). Find x, both bases and the midsegment.

Problem 14 Isosceles trapezoid ★★★

In isosceles trapezoid ABCD, one base angle measures 72°. The diagonals measure 2x + 9 and 4x − 7. Find the other angles of the trapezoid and the length of each diagonal.

Problem 15 Building a kite ★★★

A kite maker builds a kite with a horizontal crossbar of 24 inches. Two sides at the top measure 15 inches and the two sides at the bottom measure 20 inches. The long spine is perpendicular to the crossbar. Find the length of the spine and the area of the kite.

Problem 16 Garden bed fence ★★★

A parallelogram-shaped garden bed has sides of 18 feet and 11.5 feet, and one corner measures 65°. Find the other three corner angles, the perimeter, and the cost of fencing at $8.50 per foot.

Problem 17 Prove the diagonals bisect each other ★★★

Given: ABCD is a parallelogram with diagonals meeting at E. Prove: AE ≅ CE and BE ≅ DE. Write a two-column proof.

Problem 18 Prove the converse ★★★

Given: AB ≅ CD and AD ≅ BC in quadrilateral ABCD. Prove: ABCD is a parallelogram. Draw diagonal AC and write a two-column proof.

Problem 19 Prove rectangle diagonals congruent ★★★

Quadrilateral PQRS is a rectangle with diagonals PR and QS. Prove that the two diagonals have the same length by writing a two-column proof.

Problem 20 Coordinate proof of a rhombus ★★★

Show that the quadrilateral with vertices A(0, 0), B(4, 3), C(9, 3) and D(5, 0) is a rhombus, and show that its diagonals are perpendicular.