Worksheets · Geometry

Classifying quadrilaterals worksheet

Work out the four sides as vectors. Equal slopes mean parallel, equal lengths mean equal sides, and a zero dot product means a right angle, and those three tests separate every quadrilateral there is. Other questions name the shape from its diagonals or its marks, or ask whether one kind is always, sometimes or never another.

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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Classifying Quadrilaterals

Date Period

Answer each question.

  1. Name the quadrilateral from its vertices

    Name the quadrilateral: (−6,−1), (2,−1), (2,2), (−6,2).
  2. Name the quadrilateral: (3,−25), (23,−4), (3,17), (−17,−4).
  3. Name the quadrilateral: (−3,1), (3,1), (3,7), (−3,7).
  4. Name the quadrilateral: (−2,−6), (1,−6), (1,−3), (−2,−3).

  1. Name the quadrilateral from its properties

    A quadrilateral: It has exactly one pair of parallel sides, and its legs are not congruent. Give its most specific name.
  2. A quadrilateral: Both pairs of opposite sides are parallel, it has four right angles, and its adjacent sides are not congruent. Give its most specific name.
  3. A quadrilateral: It has four congruent sides and four right angles. Give its most specific name.
  4. A quadrilateral: It has one pair of opposite sides that are both parallel and congruent, and no right angles or congruent adjacent sides. Give its most specific name.

  1. Decide: always, sometimes or never

    Always, sometimes or never: A trapezoid is    a rhombus. (Here a trapezoid has exactly one pair of parallel sides.)
  2. Always, sometimes or never: A rectangle is    a rhombus.
  3. Always, sometimes or never: A rectangle is    a quadrilateral.
  4. Always, sometimes or never: A rhombus is    a parallelogram.

  1. Classify a quadrilateral using slopes and side lengths

    Classify quadrilateral ABCD with A(0,2), B(−1,0), C(−3,−1), D(−2,1) as exactly as you can. Use slopes and side lengths.
  2. Classify quadrilateral ABCD with A(−2,−4), B(−5,−3), C(−4,−6), D(−1,−7) as exactly as you can. Use slopes and side lengths.
  3. Classify quadrilateral ABCD with A(0,0), B(−4,3), C(−6,7), D(−2,4) as exactly as you can. Use slopes and side lengths.
  4. Classify quadrilateral ABCD with A(0,−4), B(−2,−7), C(7,−13), D(9,−10) as exactly as you can. Use slopes and side lengths.

  1. Name the quadrilateral from its marks

    Give the most specific name for the quadrilateral.
  2. Give the most specific name for the quadrilateral.
  3. Give every special name that fits the quadrilateral.
  4. Give every special name that fits the quadrilateral.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Classifying QuadrilateralsAnswer keyVersion 1

Date Period

Answer each question.

  1. Name the quadrilateral from its vertices

    Name the quadrilateral: (−6,−1), (2,−1), (2,2), (−6,2).Rectangle
  2. Name the quadrilateral: (3,−25), (23,−4), (3,17), (−17,−4).Rhombus
  3. Name the quadrilateral: (−3,1), (3,1), (3,7), (−3,7).Square
  4. Name the quadrilateral: (−2,−6), (1,−6), (1,−3), (−2,−3).Square

  1. Name the quadrilateral from its properties

    A quadrilateral: It has exactly one pair of parallel sides, and its legs are not congruent. Give its most specific name.Trapezoid
  2. A quadrilateral: Both pairs of opposite sides are parallel, it has four right angles, and its adjacent sides are not congruent. Give its most specific name.Rectangle
  3. A quadrilateral: It has four congruent sides and four right angles. Give its most specific name.Square
  4. A quadrilateral: It has one pair of opposite sides that are both parallel and congruent, and no right angles or congruent adjacent sides. Give its most specific name.Parallelogram

  1. Decide: always, sometimes or never

    Always, sometimes or never: A trapezoid is    a rhombus. (Here a trapezoid has exactly one pair of parallel sides.)Never
  2. Always, sometimes or never: A rectangle is    a rhombus.Sometimes
  3. Always, sometimes or never: A rectangle is    a quadrilateral.Always
  4. Always, sometimes or never: A rhombus is    a parallelogram.Always

  1. Classify a quadrilateral using slopes and side lengths

    Classify quadrilateral ABCD with A(0,2), B(−1,0), C(−3,−1), D(−2,1) as exactly as you can. Use slopes and side lengths.Rhombus: all sides 5, AB‾⊥̸BC‾
  2. Classify quadrilateral ABCD with A(−2,−4), B(−5,−3), C(−4,−6), D(−1,−7) as exactly as you can. Use slopes and side lengths.Rhombus: all sides 10, AB‾⊥̸BC‾
  3. Classify quadrilateral ABCD with A(0,0), B(−4,3), C(−6,7), D(−2,4) as exactly as you can. Use slopes and side lengths.Parallelogram: opposite sides parallel, AB=5, BC=25, AB‾⊥̸BC‾
  4. Classify quadrilateral ABCD with A(0,−4), B(−2,−7), C(7,−13), D(9,−10) as exactly as you can. Use slopes and side lengths.Rectangle: AB=13, BC=313, AB‾⊥BC‾

  1. Name the quadrilateral from its marks

    Give the most specific name for the quadrilateral.Rhombus
  2. Give the most specific name for the quadrilateral.Trapezoid
  3. Give every special name that fits the quadrilateral.Parallelogram
  4. Give every special name that fits the quadrilateral.Kite

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

(0,0), (4,0), (4,4), (0,4)

  1. All four sides have length 4.
  2. Both pairs are parallel.
  3. And they meet at right angles.

The answer is Square.

Where students go wrong

Stopping at parallelogram. A square is one too, and so is a rhombus and a rectangle; the question wants the most specific name that fits, so keep testing.

Also called identifying quadrilaterals, quadrilaterals on the coordinate plane or square rectangle rhombus parallelogram.

What you can put on this worksheet

Naming from the corners
Name the quadrilateral: (−1,1), (4,1), (4,4), (−1,4). → Rectangle
Most specific name from its properties
A quadrilateral: Its diagonals bisect each other, but are neither congruent nor perpendicular. Give its most specific name. → Parallelogram
Always, sometimes or never
Always, sometimes or never: A trapezoid is    a square. (Here a trapezoid has exactly one pair of parallel sides.) → Never
Classify from the vertices
Classify quadrilateral ABCD with A(−3,3), B(0,1), C(6,10), D(3,12) as exactly as you can. Use slopes and side lengths. → Rectangle: AB=13, BC=313, AB‾⊥BC‾
Name the quadrilateral from its marks
Give the most specific name for the quadrilateral. — a quadrilateral with its marks → Trapezoid
Name it from its side lengths and angles
Which special quadrilateral is this? Give the most specific name. — a polygon with side lengths and angles marked, labeled 11, 10, 11, 10, 119°, 61° → Parallelogram

Questions about these worksheets

Yes. Every classifying quadrilaterals sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the classifying quadrilaterals questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 6: naming from the corners, most specific name from its properties, always, sometimes or never, classify from the vertices, name the quadrilateral from its marks and name it from its side lengths and angles. Tick as many as you want and set how many of each, or let it spread them evenly.

Stopping at parallelogram. A square is one too, and so is a rhombus and a rectangle; the question wants the most specific name that fits, so keep testing.