Reference / Curriculum / 3B / Chapter 12

3B · Chapter 12 · Lesson 4

Triangles

Classify and describe triangles by visible geometric properties.

MATH-3B-C12-L04Independent and tutor-supported

Today's mathematical question

A triangle has side lengths 5, 5, and 7 units. Classify it by its side lengths.

Learning target

Classify and describe triangles by visible geometric properties.

Before starting: Prior lesson: Right Angles. 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

    An angle measures 65°. Is it acute, right, or obtuse?

    Reveal explanation

    Answer: acute

    Compare 65° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.

    65°
    Angle of 65 degrees; angle size depends on rotation, not ray length.
  2. P2

    An angle measures 98°. Is it acute, right, or obtuse?

    Reveal explanation

    Answer: obtuse

    Compare 98° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.

    98°
    Angle of 98 degrees; angle size depends on rotation, not ray length.
  3. P3

    An angle measures 110°. Is it acute, right, or obtuse?

    Reveal explanation

    Answer: obtuse

    Compare 110° with 90°: angles smaller are acute, exactly 90° are right, and larger but less than 180° are obtuse.

    110°
    Angle of 110 degrees; angle size depends on rotation, not ray length.

Learn and understand

A triangle is a closed shape made from three straight sides. Its corners are vertices, and the sides meet at three angles. A shape with a curved side is not a triangle. Triangles can look tall, wide, rotated, or upside down without changing their number of sides. A triangle must be closed and have three straight sides. A bent open chain of three segments is not yet a triangle. Trace the boundary and count the vertices.

Represent it three ways

  1. Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
  2. Pictorial: Draw a triangle with a ruler, then count three straight sides and three vertices. Compare it with a three-sided open figure and a curved figure.
  3. Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.

Important vocabulary

triangle
closed three-sided polygon
vertex
corner where sides meet
polygon
closed figure with straight sides

Fully worked examples and checks

Try each new understanding check before revealing the explanation.

Worked example 1

Explore, calculate, verify

A triangle has side lengths 5, 5, and 7 units. Classify it by its side lengths.

  1. Identify the whole, the units, and what the question asks.
  2. Isosceles means exactly two equal sides. These lengths satisfy the triangle inequality.
  3. Check that the answer uses the right units and makes sense.

Answer: isosceles

Check your understanding 1

A triangle has side lengths 8, 8, and 8 units. Classify it by its side lengths.

Reveal answer and explanation

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

Worked example 2

Explore, calculate, verify

A triangle has side lengths 13, 13, and 15 units. Classify it by its side lengths.

  1. Identify the whole, the units, and what the question asks.
  2. Isosceles means exactly two equal sides. These lengths satisfy the triangle inequality.
  3. Check that the answer uses the right units and makes sense.

Answer: isosceles

Check your understanding 2

A triangle has side lengths 7, 8, and 9 units. Classify it by its side lengths.

Reveal answer and explanation

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

Worked example 3

Explore, calculate, verify

A triangle has side lengths 3, 3, and 3 units. Classify it by its side lengths.

  1. Identify the whole, the units, and what the question asks.
  2. Equilateral means three equal sides. These lengths satisfy the triangle inequality.
  3. Check that the answer uses the right units and makes sense.

Answer: equilateral

Check your understanding 3

A triangle has side lengths 3, 3, and 5 units. Classify it by its side lengths.

Reveal answer and explanation

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

Guided · 5 questions

Guided practice

Keep the model and earlier examples visible while practising.

  1. G1

    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.

  2. G2

    A triangle has side lengths 11, 11, and 11 units. Classify it by its side lengths.

    Reveal explanation

    Answer: equilateral

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

  3. G3

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

    Reveal explanation

    Answer: equilateral

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

  4. G4

    A triangle has side lengths 11, 12, and 13 units. Classify it by its side lengths.

    Reveal explanation

    Answer: scalene

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

  5. G5

    A triangle has side lengths 12, 12, and 14 units. Classify it by its side lengths.

    Reveal explanation

    Answer: isosceles

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

Independent · 8 questions

Independent practice

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

  1. I1

    A triangle has side lengths 4, 5, and 6 units. Classify it by its side lengths.

    Reveal explanation

    Answer: scalene

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

  2. I2

    A triangle has side lengths 10, 11, and 12 units. Classify it by its side lengths.

    Reveal explanation

    Answer: scalene

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

  3. I3

    A triangle has side lengths 3, 4, and 5 units. Classify it by its side lengths.

    Reveal explanation

    Answer: scalene

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

  4. I4

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

    Reveal explanation

    Answer: equilateral

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

  5. I5

    A triangle has side lengths 8, 8, and 10 units. Classify it by its side lengths.

    Reveal explanation

    Answer: isosceles

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

  6. I6

    A triangle has side lengths 11, 11, and 13 units. Classify it by its side lengths.

    Reveal explanation

    Answer: isosceles

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

  7. I7

    A triangle has side lengths 6, 6, and 8 units. Classify it by its side lengths.

    Reveal explanation

    Answer: isosceles

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

  8. I8

    A triangle has side lengths 9, 9, and 11 units. Classify it by its side lengths.

    Reveal explanation

    Answer: isosceles

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

Challenge · 2 questions

Challenge and error analysis

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

  1. C1

    A triangle has side lengths 7, 7, and 8. Explain why it is isosceles but not equilateral.

    Reveal explanation

    Answer: Isosceles

    It has exactly two equal sides. An equilateral triangle requires all three sides equal.

  2. C2

    Can three line segments of lengths 2, 3, and 8 units make a triangle? Explain.

    Reveal explanation

    Answer: No

    The two shorter lengths total only 5, which cannot reach across a segment of length 8.

Exit · 3 questions

Exit check

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

  1. E1

    A triangle has side lengths 6, 7, and 8 units. Classify it by its side lengths.

    Reveal explanation

    Answer: scalene

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

  2. E2

    A triangle has side lengths 10, 10, and 10 units. Classify it by its side lengths.

    Reveal explanation

    Answer: equilateral

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

  3. E3

    A triangle has side lengths 10, 10, and 12 units. Classify it by its side lengths.

    Reveal explanation

    Answer: isosceles

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

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