Reference / Curriculum / 3B / Chapter 12

3B · Chapter 12 · Lesson 6

Properties of Quadrilaterals

Distinguish parallelograms, rectangles, squares, and rhombuses by properties.

MATH-3B-C12-L06Independent and tutor-supported

Today's mathematical question

Identify the most specific shape: a quadrilateral has four right angles and four equal sides of 5 cm.

Learning target

Distinguish parallelograms, rectangles, squares, and rhombuses by properties.

Before starting: Prior lesson: Properties of Triangles. Try the warm-up independently.

Prerequisite · 3 questions

Check earlier skills first

These are earlier ideas you need for today; revisit them if they are difficult.

  1. P1

    A triangle has side lengths 4, 4, and 6 units. Classify it by its side lengths.

    Reveal explanation

    Answer: isosceles

    Isosceles means exactly two equal sides. These lengths satisfy the triangle inequality.

  2. P2

    A triangle has side lengths 14, 15, and 16 units. Classify it by its side lengths.

    Reveal explanation

    Answer: scalene

    Scalene means no equal sides. These lengths satisfy the triangle inequality.

  3. P3

    A triangle has side lengths 14, 14, and 14 units. Classify it by its side lengths.

    Reveal explanation

    Answer: equilateral

    Equilateral means three equal sides. These lengths satisfy the triangle inequality.

Learn and understand

Quadrilaterals are closed polygons with four straight sides. A parallelogram has two pairs of parallel opposite sides. Rectangles are parallelograms with four right angles, and squares are rectangles with four equal sides. A rhombus has four equal sides; it may or may not have right angles. A square is a special rectangle because it has four right angles; it is also a special rhombus because it has four equal sides. Classifications may overlap.

Represent it three ways

  1. Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
  2. Pictorial: Draw each shape, mark right angles and parallel sides, and compare properties. Explain how a square can belong to several families.
  3. Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.

Important vocabulary

quadrilateral
closed four-sided polygon
parallel lines
lines never meeting
rhombus
four equal sides

Fully worked examples and checks

Try each new understanding check before revealing the explanation.

Worked example 1

Explore, calculate, verify

Identify the most specific shape: a quadrilateral has four right angles and four equal sides of 5 cm.

  1. Identify the whole, the units, and what the question asks.
  2. The shape is a square. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.
  3. Check that the answer uses the right units and makes sense.

Answer: square

Check your understanding 1

Identify the most specific shape: a quadrilateral has four right angles, adjacent side lengths 10 cm and 12 cm.

Reveal answer and explanation

rectangle — The shape is a rectangle. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.

Worked example 2

Explore, calculate, verify

Identify the most specific shape: a quadrilateral has four right angles and four equal sides of 3 cm.

  1. Identify the whole, the units, and what the question asks.
  2. The shape is a square. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.
  3. Check that the answer uses the right units and makes sense.

Answer: square

Check your understanding 2

Identify the most specific shape: a quadrilateral has four equal sides of 10 cm but no right angles.

Reveal answer and explanation

rhombus — The shape is a rhombus. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.

Worked example 3

Explore, calculate, verify

Identify the most specific shape: a quadrilateral has four right angles, adjacent side lengths 12 cm and 14 cm.

  1. Identify the whole, the units, and what the question asks.
  2. The shape is a rectangle. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.
  3. Check that the answer uses the right units and makes sense.

Answer: rectangle

Check your understanding 3

Identify the most specific shape: a quadrilateral has two pairs of parallel sides, side lengths 6 and 8 cm, and no right angles.

Reveal answer and explanation

parallelogram — The shape is a parallelogram. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.

Guided · 5 questions

Guided practice

Keep the model and earlier examples visible while practising.

  1. G1

    Identify the most specific shape: a quadrilateral has two pairs of parallel sides, side lengths 9 and 11 cm, and no right angles.

    Reveal explanation

    Answer: parallelogram

    The shape is a parallelogram. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.

  2. G2

    Identify the most specific shape: a quadrilateral has four right angles and four equal sides of 12 cm.

    Reveal explanation

    Answer: square

    The shape is a square. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.

  3. G3

    Identify the most specific shape: a quadrilateral has two pairs of parallel sides, side lengths 8 and 10 cm, and no right angles.

    Reveal explanation

    Answer: parallelogram

    The shape is a parallelogram. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.

  4. G4

    Identify the most specific shape: a quadrilateral has four equal sides of 3 cm but no right angles.

    Reveal explanation

    Answer: rhombus

    The shape is a rhombus. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.

  5. G5

    Identify the most specific shape: a quadrilateral has four equal sides of 6 cm but no right angles.

    Reveal explanation

    Answer: rhombus

    The shape is a rhombus. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.

Independent · 8 questions

Independent practice

Work these without hints and explain the method used. Write answers on paper.

  1. I1

    Identify the most specific shape: a quadrilateral has four right angles and four equal sides of 11 cm.

    Reveal explanation

    Answer: square

    The shape is a square. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.

  2. I2

    Identify the most specific shape: a quadrilateral has two pairs of parallel sides, side lengths 10 and 12 cm, and no right angles.

    Reveal explanation

    Answer: parallelogram

    The shape is a parallelogram. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.

  3. I3

    Identify the most specific shape: a quadrilateral has four equal sides of 5 cm but no right angles.

    Reveal explanation

    Answer: rhombus

    The shape is a rhombus. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.

  4. I4

    Identify the most specific shape: a quadrilateral has four right angles, adjacent side lengths 8 cm and 10 cm.

    Reveal explanation

    Answer: rectangle

    The shape is a rectangle. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.

  5. I5

    Identify the most specific shape: a quadrilateral has four equal sides of 9 cm but no right angles.

    Reveal explanation

    Answer: rhombus

    The shape is a rhombus. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.

  6. I6

    Identify the most specific shape: a quadrilateral has two pairs of parallel sides, side lengths 11 and 13 cm, and no right angles.

    Reveal explanation

    Answer: parallelogram

    The shape is a parallelogram. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.

  7. I7

    Identify the most specific shape: a quadrilateral has four right angles, adjacent side lengths 6 cm and 8 cm.

    Reveal explanation

    Answer: rectangle

    The shape is a rectangle. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.

  8. I8

    Identify the most specific shape: a quadrilateral has two pairs of parallel sides, side lengths 4 and 6 cm, and no right angles.

    Reveal explanation

    Answer: parallelogram

    The shape is a parallelogram. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.

Challenge · 2 questions

Challenge and error analysis

Go beyond arithmetic: justify a claim, correct reasoning, or connect two representations.

  1. C1

    A square is rotated on the paper. Does its shape classification change? Explain.

    Reveal explanation

    Answer: No

    A rotation preserves its equal side lengths and four right angles.

  2. C2

    A quadrilateral has four equal sides but no right angles. Can it be a square? What more specific shape is it?

    Reveal explanation

    Answer: Not a square; rhombus

    A square requires right angles. A four-equal-sided quadrilateral without right angles is a rhombus.

Exit · 3 questions

Exit check

Solve independently, then return on another day to check retention.

  1. E1

    Identify the most specific shape: a quadrilateral has four right angles, adjacent side lengths 9 cm and 11 cm.

    Reveal explanation

    Answer: rectangle

    The shape is a rectangle. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.

  2. E2

    Identify the most specific shape: a quadrilateral has four right angles and four equal sides of 7 cm.

    Reveal explanation

    Answer: square

    The shape is a square. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.

  3. E3

    Identify the most specific shape: a quadrilateral has four equal sides of 12 cm but no right angles.

    Reveal explanation

    Answer: rhombus

    The shape is a rhombus. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.

Continue →Complete answer key