Geometry Parallelograms and Quadrilaterals Worksheet (PDF)

Geometry math worksheet: Parallelograms and Quadrilaterals – Maths PDF

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This parallelograms practice worksheet for Geometry covers parallelograms and quadrilaterals (Common Core G-CO.C.11), with a free PDF to print.

These 20 problems practice parallelograms, rectangles, rhombuses, kites and trapezoids (Common Core G-CO.C.11). The first problems are quick one-step checks of the definitions and formulas from the lesson. The middle problems ask for diagrams, equations and careful reasoning in the style of a high school Geometry class. The last six problems are applications with frames, stands, kites and coordinates.

Geometry · Common Core State Standards: G-CO.C.11

Parallelograms practice worksheet: exercises 1 to 10

Exercise 1 – Opposite sides

Parallelogram ABCD.

In parallelogram ABCD, AB = 14 and BC = 9. Find CD and AD.

Exercise 2 – Opposite angles

In parallelogram WXYZ, \(m\angle W = 123^{\circ}\). Find \(m\angle Y\) and \(m\angle X\).

Exercise 3 – Consecutive angles with x

In parallelogram ABCD, \(m\angle A = (4x + 10)^{\circ}\) and \(m\angle B = (2x + 20)^{\circ}\). Find x and both angles.

Exercise 4 – Diagonals bisect

Diagonals meet at E.

The diagonals of parallelogram ABCD meet at E. AE = 7 and BE = 5.5. Find AC and BD.

Exercise 5 – Diagonals with x

In parallelogram ABCD the diagonals meet at E. \(AE = 3x + 1\) and \(EC = 5x – 9\). Find x and AC.

Exercise 6 – Sides with x

In parallelogram ABCD, \(AB = 4x – 3\) and \(CD = 2x + 9\). Find x and AB.

Exercise 7 – Perimeter

A parallelogram has sides of 8 inches and 13 inches. Find its perimeter.

Exercise 8 – Fourth vertex

Parallelogram ABCD.

Three vertices of parallelogram ABCD are A(0, 0), B(5, 1) and D(1, 4). Find C.

Exercise 9 – Rectangle diagonals

A rectangle has congruent diagonals.

In rectangle ABCD, \(AC = 2x + 6\) and \(BD = 4x – 10\). Find x and AC.

Exercise 10 – Rectangle diagonal

A rectangle is 9 units long and 12 units wide. Find the length of its diagonal.

Exercises 11 and up

Exercise 11 – Rhombus side

Rhombus with diagonals 16 and 30.

The diagonals of a rhombus are 16 and 30. Find the side length and the perimeter.

Exercise 12 – Rhombus angles

In rhombus ABCD, \(m\angle A = 64^{\circ}\). Find \(m\angle B\) and the angle that diagonal AC makes with side AB.

Exercise 13 – Square diagonal

A square has side length 10. Find its diagonal and the angle the diagonal makes with a side.

Exercise 14 – Kite angles

Kite ABCD.

In kite ABCD, \(m\angle A = 70^{\circ}\) and \(m\angle B = m\angle D = 95^{\circ}\). Find \(m\angle C\).

Exercise 15 – Isosceles trapezoid

Isosceles trapezoid ABCD.

In isosceles trapezoid ABCD with bases AB and DC, \(m\angle D = 72^{\circ}\). Find the other three angles.

Exercise 16 – Trapezoid midsegment

The bases of a trapezoid are 10 and 24. Find the length of the midsegment, which is the average of the bases.

Exercise 17 – Classify from coordinates

Quadrilateral ABCD.

The vertices of ABCD are A(0, 0), B(4, 3), C(8, 0) and D(4, -3). Show that ABCD is a rhombus but not a square.

Exercise 18 – Laptop stand

A laptop stand has a parallelogram linkage with sides 14 inches and 9 inches. When the angle at A is 72°, find the other three angles and the perimeter.

Exercise 19 – Picture frame

A rectangular picture frame is 24 inches wide and 18 inches tall. A carpenter checks that the corners are square by measuring the diagonals. What should each diagonal measure?

Exercise 20 – Festival kite

Kite with perpendicular diagonals.

A kite has perpendicular diagonals of 60 cm and 40 cm. Find its area.

Key facts behind this parallelograms practice worksheet

Key facts

Parallelogram: opposite sides congruent, opposite angles congruent, diagonals bisect each other.
Consecutive angles of a parallelogram add to 180 degrees.
Rectangle: four right angles and congruent diagonals.
Rhombus: four congruent sides and perpendicular diagonals that bisect the angles.
The angles of any quadrilateral add to 360 degrees.

How to use this parallelograms practice worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the parallelograms practice worksheet as a PDF with the button below and keep it with your notes.

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