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      Constructing triangles

      Lesson details

      Learning outcome

      I can use intersecting circles to construct triangles from given lengths.

      Key learning points

      1. A construction is an accurate drawing made using geometrical properties.
      2. A scalene triangle can be constructed using intersecting circles with different radii.
      3. An equilateral triangle can be constructed using intersecting circles with equal radii.
      4. An isosceles triangle can be constructed using intersecting circles.

      Keywords

      • Scalene triangle - Scalene triangles have three different-sized angles and three edges of different lengths.

      • Isosceles triangle - Isosceles triangles have two equal-sized angles. Two of the edges are equal in length.

      • Equilateral triangle - Equilateral triangles have three equal-sized angles and three edges of equal length. They are regular triangles.

      • Radius - The radius is any line segment that joins the centre of a circle to any point on its circumference.

      Common misconception

      Pupils may avoid using the pair of compasses and opt for a ruler instead.

      Emphasise the efficiency and accuracy of using compasses instead of a ruler in the construction of their triangles.

      Teacher tip

      Random number generators, dice or playing cards can be used to select three edge lengths for pupils to construct. Pupils can consider if a triangle can be constructed before attempting to.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

      6 Questions

      Q1.
      Match the angle size to the type of angle.

      Correct Answer:$$12^\circ$$,acute angle
      Correct Answer:$$90^\circ$$,right angle
      Correct Answer:$$138^\circ$$,obtuse angle
      Correct Answer:$$305^\circ$$,reflex angle

      Q2.
      Which of these sketched triangles are definitely isosceles?

      Correct Answer: An image in a quiz
      An image in a quiz
      An image in a quiz
      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz

      Q3.
      Lucas has used a centimetre ruler to draw a line of 8.2 cm. Which image shows his line?

      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz
      An image in a quiz
      An image in a quiz

      Q4.
      Which of these shows the best set up of a pair of compasses?

      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz
      An image in a quiz

      Q5.
      An arc of a circle is part of the circle’s .

      Correct Answer: circumference

      Q6.
      A triangle has a perimeter of 65 mm. Two of the edges are 23 mm and 26 mm respectively. How long is the third edge of the triangle?

      15 mm
      Correct answer: 16 mm
      17 mm
      18 mm
      19 mm

      6 Questions

      Q1.
      Which description matches this sketch?

      An image in a quiz
      Triangle PQR, where PQ = 7 cm, PR = 12 cm and QR = 14 cm
      Triangle PQR, where PQ = 7 cm, PR = 14 cm and QR = 12 cm
      Correct answer: Triangle PQR, where PQ = 12 cm, PR = 14 cm and QR = 7 cm
      Triangle PQR, where PQ = 14 cm, PR = 7 cm and QR = 12 cm
      Triangle PQR, where PQ = 14 cm, PR = 12 cm and QR = 7 cm

      Q2.
      When constructing a triangle from three edge lengths, we use a pair of compasses to draw circles.

      Correct Answer: intersecting

      Q3.
      Which of the following shows a partial construction of an equilateral triangle?

      An image in a quiz
      An image in a quiz
      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz

      Q4.
      Which of the following lengths could be the edge lengths of a triangle?

      Correct answer: 3 cm, 4 cm and 5 cm
      3 cm, 3 cm and 6 cm
      Correct answer: 8 cm, 8 cm and 8 cm
      7 cm, 9 cm and 18 cm
      Correct answer: 9 cm, 9 cm and 14 cm

      Q5.
      Which of the points C, D or E when connected to AB would create a triangle with three edges of different lengths?

      An image in a quiz
      Correct answer: C
      D
      E

      Q6.
      Triangle ABE is an triangle.

      An image in a quiz
      Correct Answer: isosceles

      To help you plan your 8 maths lesson on: Constructing triangles, download all teaching resources for free and adapt to suit your pupils' needs...