Year 8 - Properties of quadrilaterals - Free practice

Year 8 Properties of Quadrilaterals Worksheets & Practice

Use congruent triangles and angle properties to unlock every quadrilateral family.

Quick answer

What are the properties of quadrilaterals and how do you prove them?

Quadrilateral properties follow from congruent triangles and angle rules. A parallelogram's opposite sides and angles are equal, and its diagonals bisect each other, provable by showing the diagonal creates two congruent triangles (AAS or SAS). Rectangles, rhombuses and squares add extra properties. The angle sum of any quadrilateral is 360°.

Generate a free maths worksheet

Six questions across Foundation, Standard and Extension, with full worked solutions, written to the Australian Curriculum.

Want more than a worksheet?

Practice built from mistakes.

A worksheet on Year 8 properties of quadrilaterals is a good start. Tuterly goes further: it turns any question students get wrong into fresh practice, at the right level, on what’s likely to be in the next test or exam.

~90% of Bayside Academics students using it weekly improved their test marks

Of the Bayside Academics students who used Tuterly at least once a week, about 90% improved their school test marks.

Based on the actual school test marks of 100+ Bayside Academics students (in person and online) in Years 7 to 10, before and after using Tuterly at least once a week. How we measured this

Free worksheet Tuterly

The questionsFree worksheetThe same questions for every student on this topic.TuterlyWritten from the questions they got wrong in homework and school tests, at their level.

How manyFree worksheetOne sheet at a time.TuterlyAs many fresh questions as they need, each one different, never just the numbers swapped.*

Before a testFree worksheetPick a topic and hope it’s the right one.TuterlyA practice test covering every part of the topic. Upload the term planner and it focuses on what’s coming up.

MarkingFree worksheetCheck the answer key yourself.TuterlyMarked as they go, with the exact step that went wrong explained.

ProgressFree worksheetNothing is saved.TuterlyEvery question tracked until it’s mastered, and a weekly review for parents.

For Years 7 to 10: $8.99 a week or $29.99 a month at the launch price (from 1 April 2027, $17.99 a week or $59.99 a month), with a 7-day free trial on the monthly plan only. Better marks in 6 months, or your money back.

Or try it free now on one of their questions →

Coming soon on iPhone. Android soon after.

Free to download · 7-day free trial on monthly · Years 7 to 10 maths · On iPhone. Android coming soon

* With a subscription. Fair use applies: up to 80 snapped questions and 120 new practice questions a day per student.

Worked examples

Year 8 properties of quadrilaterals: worked examples

Three examples, from a standard question to a worded problem. Have a go at each one before you open the solution.

Example 1 · Finding unknown angles in a quadrilateral
A quadrilateral has three known interior angles of $112°$ , $75°$ and $96°$ . Find the fourth interior angle.
Show worked solution
Key idea: The interior angles of any quadrilateral add to $360°$ .
1. Write the angle sum equation:
  $112 + 75 + 96 + x = 360$
2. Add the three known angles:
  $283 + x = 360$
3. Solve for $x$ :
  $x = 360 - 283 = 77$
Answer: The fourth angle is $77°$ .
Example 2 · Using parallelogram properties to find side lengths and angles
In parallelogram $ABCD$ , side $AB = 3x - 1$ cm, side $CD = 2x + 4$ cm, and angle $DAB = 65°$ . Find the value of $x$ , the length of $AB$ , and the size of angle $BCD$ .
Show worked solution
Key idea: In a parallelogram, opposite sides are equal and co-interior (same-side) angles are supplementary, adding to $180°$ .
1. Set opposite sides equal and solve for $x$ :
  $\begin{gathered}3x - 1 = 2x + 4 \\ x = 5\end{gathered}$
2. Find the length of $AB$ :
  $AB = 3(5) - 1 = 14 \text{ cm}$
3. Angle $BCD$ is opposite to angle $DAB$ , so opposite angles in a parallelogram are equal:
  $\angle BCD = \angle DAB = 65°$
Answer: $x = 5$ , $AB = 14$ cm, $\angle BCD = 65°$ .
Example 3 · Applying diagonal properties of a rhombus
A garden bed is shaped as a rhombus $PQRS$ with side length $8$ m. The gardener stretches two string lines along the diagonals, which cross at point $M$ . She measures $PM = 6$ m. Find the length of the other half-diagonal $QM$ , and find the full length of diagonal $QS$ .
Show worked solution
Key idea: The diagonals of a rhombus bisect each other at right angles, so triangle $PMQ$ is right-angled at $M$ .
1. In right-angled triangle $PMQ$ , the hypotenuse is the side of the rhombus:
  $PQ = 8 \text{ m}, PM = 6 \text{ m}$
2. Apply Pythagoras' theorem to find $QM$ :
  $\begin{gathered}QM^2 = PQ^2 - PM^2 = 8^2 - 6^2 = 64 - 36 = 28 \\ QM = \sqrt{28} = 2\sqrt{7} \approx 5.29 \text{ m}\end{gathered}$
3. The diagonals bisect each other, so $SM = QM$ . The full length of diagonal $QS$ is:
  $QS = 2 \times QM = 4\sqrt{7} \approx 10.58 \text{ m}$
Answer: $QM = 2\sqrt{7}$ m (approximately $5.29$ m); diagonal $QS = 4\sqrt{7}$ m (approximately $10.58$ m).

Common mistakes

Where students usually lose marks

Confusing co-interior and opposite angles in a parallelogram

In parallelogram $ABCD$ , if $\angle DAB = 70°$ , a student writes $\angle ABC = 70°$ (same as the opposite angle).

Opposite angles in a parallelogram are equal, but adjacent angles are co-interior (between parallel lines) and add to $180°$ . Always check whether the angles share a side: if they do, they add to $180°$ ; if they face each other, they are equal.

Assuming all parallelograms have equal diagonals

A student states that the diagonals of a parallelogram are equal because "diagonals always bisect each other."

Diagonals bisect each other in any parallelogram, but they are only equal in length in rectangles and squares. In a general parallelogram or rhombus the two diagonals have different lengths. Always check which special properties belong to which shape.

Forgetting that the angle sum of a quadrilateral is 360°, not 180°

A student writes $x + 80 + 90 + 75 = 180$ to find the missing angle in a quadrilateral.

The angle sum of $180°$ applies to triangles. A quadrilateral is made of two triangles, so its interior angles add to $2 \times 180° = 360°$ . Always write the equation $\text{angle sum} = 360°$ first.

Applying parallelogram properties to a trapezium

In a trapezium with one pair of parallel sides, a student assumes both pairs of opposite sides are equal.

A trapezium has only one pair of parallel sides, so opposite sides are not generally equal and opposite angles are not generally equal. Only use parallelogram properties (opposite sides equal, opposite angles equal, diagonals bisect each other) when you have confirmed both pairs of opposite sides are parallel.

Try one yourself

Your turn

In a parallelogram $ABCD$ , the diagonal $AC$ divides it into two triangles. It is known that $AB = 13$ cm, $BC = 7$ cm and $\angle ABC = 74°$ . Using the property that opposite angles of a parallelogram are equal, find $\angle ADC$ in degrees.

Got a different properties of quadrilaterals question wrong? Upload it to Tuterly and get the worked solution and a fresh one to practise, free.

About this worksheet

Why we built it

In Year 8, students move beyond naming shapes and start proving why quadrilaterals have their special properties, using congruent triangles and angle relationships as the tools. These worksheets build that reasoning step by step, from identifying matching triangles inside a parallelogram to writing clear geometric arguments, with worked solutions so students can check exactly where their logic holds or breaks.

What's covered

Sub-skills your student will practise

✓Identifying congruent triangles formed by diagonals inside quadrilaterals
✓Proving properties of parallelograms using congruence (sides, angles, diagonals)
✓Properties of rectangles, rhombuses and squares as special parallelograms
✓Angle sum of quadrilaterals and finding unknown angles
✓Properties of trapeziums and kites using angle and side relationships
✓Solving problems that require selecting and applying quadrilateral properties

From our families

Parents on the practice questions.

“Tuterly has been exactly what we needed since Tom started secondary school. Once the topic tests began, he was struggling to keep up. Now he has unlimited practice, all matched to what his class is actually covering, and his Maths results have improved noticeably.”

Rebecca M.

Year 8 · Maths

“My daughter used to leave revision until the night before. Having a platform she can dip into for fifteen minutes after dinner has completely changed that. She's calmer going into assessments, and honestly, so am I.”

Priya S.

Year 9 · Maths

“I like that I can just keep doing questions until it clicks. If I get something wrong, it shows me why, and then gives me another one like it.”

Ella, student

Year 10 · Maths

Verified parent

Frequently asked

Questions parents ask about properties of quadrilaterals

Why do Year 8 students use congruent triangles to study quadrilaterals?

Drawing a diagonal splits any quadrilateral into two triangles. If those triangles are congruent, their matching sides and angles must be equal, which is exactly how we prove that opposite sides or angles of a parallelogram are always equal.

What is the difference between a rhombus and a square in Year 8 geometry?

Both have four equal sides and diagonals that bisect each other at right angles. A square also has four right angles, so it is a special type of rhombus. Students practise identifying which extra property makes the difference.

How do students find unknown angles in quadrilateral problems?

The interior angles of any quadrilateral add to 360 degrees. For special quadrilaterals like parallelograms or kites, extra properties such as equal opposite angles or a line of symmetry let students set up simple equations to solve for the unknown angle.

Better maths marks start with the next wrong answer.

Tuterly turns every missed maths question into practice tailored towards the student, not just a generic worksheet.