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Triangle Classification Worksheet

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Triangle Classification Worksheet

You are helping plan a triangular design for a community garden. Classify triangles by their side lengths and angles, then use the rules to check designs. A triangle’s interior angles add to 180°. By sides: equilateral has 3 equal sides, isosceles has at least 2 equal sides, and scalene has no equal sides. By angles: acute has 3 acute angles, right has one 90° angle, and obtuse has one angle greater than 90°.

Classify the designs

Use the given measurements. Some triangles can be classified once by sides and once by angles.

1.Garden bed A has side lengths 5 m, 5 m and 5 m. Classify it by its sides.
2.A triangular sign has angles of 38°, 52° and 90°. Classify it by its angles.
  • Acute
  • Right
  • Obtuse
  • Equilateral
3.A support bracket has angles of 112°, 34° and 34°. Classify it by angles and by sides.
4.A triangular paving panel has side lengths 6 cm, 8 cm and 11 cm. Classify it by its sides.
  • Equilateral
  • Isosceles
  • Scalene

Check the maths

A triangle must satisfy both the angle-sum rule and the side-length rule: the sum of any two side lengths must be greater than the third.

5.A designer proposes a triangle with angles 45°, 65° and 80°. Is this possible? Explain using the angle-sum rule.
6.The three side lengths of a proposed edging are 4 m, 7 m and 12 m. Can they form a triangle? Show the check that proves your answer.
7.A triangular frame has angles of 72° and 48°. Find its third angle, then classify the triangle by angles.
8.True or false: A triangle can be both isosceles and right-angled. Give one set of angles to support your answer.
TrueFalse

Design and explain

Sketch possible triangle designs in the space provided. Keep the measurements and classification consistent.

9.Sketch a scalene right-angled triangle. Label its angles 90°, 35° and 55°. Explain why it is scalene.
10.Create a triangle that is both isosceles and obtuse. Write a possible set of angles and explain why it works.
11.A friend says, “Every isosceles triangle is acute.” Do you agree? Give a counterexample or explain why the statement is correct.

2 printable pages

  • Triangle classification rules, a garden design illustration, and questions on classifying triangles by side lengths and angles.

    Page 1

  • Triangle angle-sum and side-length reasoning, with sketch challenges for scalene right and isosceles obtuse triangles.

    Page 2

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