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      Formalising understanding of triangles from KS2

      Lesson details

      Learning outcome

      I can classify triangles and know their relevant properties.

      Key learning points

      1. An equilateral triangle is a regular triangle and has particular properties.
      2. A scalene triangle has specific properties.
      3. An isosceles triangle has properties including a line of symmetry that splits it into two congruent triangles.
      4. A right-angled triangle can be scalene or isosceles.

      Keywords

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

      • Scalene - Scalene triangles have three different-sized angles and three different-sized edges (sides).

      • Isosceles - Isosceles triangles have two equal-sized angles and two sides of the same length.

      • Right-angled triangle - A right-angled triangle has exactly one 90° interior angle.

      Common misconception

      The horizontal side length of an isosceles triangle is always the base side.

      The base side of an isosceles triangle can have any orientation. It is important to look at the hash marks, angle markers, or measurements.

      Teacher tip

      It's important to encourage students to be attentive and critical of the information given to them. Interior angles in a triangle sum to 180° and so other angle facts need to be used first if exterior or conjugate angles are given instead.

      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.
      TU is a line segment. $$a$$° = °.

      An image in a quiz
      Correct Answer: 37, 37°, 37 degrees, 37degrees

      Q2.
      These three angles lie around a point on a full turn. $$b$$° = °.

      An image in a quiz
      Correct Answer: 54, 54°, 54 degrees, 54degrees

      Q3.
      This diagram shows four angles around two line segments that meet at an intersection. Which of these statements are correct for angle $$c$$°?

      An image in a quiz
      Angle $$c$$° and 42° are vertically opposite.
      Correct answer: Angle $$c$$° and 42° are supplementary.
      Angle $$c$$° and 42° are conjugate.
      Angle $$c$$° is 42°.
      Correct answer: Angle $$c$$° is 138°.

      Q4.
      This diagram shows four angles around two line segments that meet at an intersection. Which of these statements are correct for angle $$d$$?

      An image in a quiz
      Correct answer: Angle $$d$$° and 42° are vertically opposite.
      Angle $$d$$° and 42° are supplementary.
      Angle $$d$$° and 42° are conjugate.
      Correct answer: Angle $$d$$° is 42°.
      Angle $$d$$° is 318°.

      Q5.
      PQ and RS are straight line segments. $$e$$° = °.

      An image in a quiz
      Correct Answer: 111, 111°, 111 degrees, 111degrees

      Q6.
      PQ and RS are straight line segments. Match each angle to its size.

      An image in a quiz
      Correct Answer:$$f$$°,155°

      155°

      Correct Answer:$$g$$°,25°

      25°

      Correct Answer:$$h$$°,65°

      65°

      Correct Answer:right angle,90°

      90°

      Correct Answer:not an angle on the diagram,45°

      45°

      Correct Answer:sum of angles on the diagram,360°

      360°

      6 Questions

      Q1.
      Which of these statements are true about this triangle?

      An image in a quiz
      Correct answer: It is a scalene triangle.
      It is a right angle triangle.
      $$a$$° = 61°
      Correct answer: $$a$$° = 82°
      $$a$$° = 90°

      Q2.
      This triangle is scalene. Which of these are possible values of $$b$$?

      An image in a quiz
      5
      6
      Correct answer: 9
      14
      Correct answer: 16

      Q3.
      Which of these statements are correct for this triangle?

      An image in a quiz
      The triangle is scalene.
      Correct answer: The triangle is isosceles.
      The triangle is right angle.
      Correct answer: $$c$$° = 48°
      It is impossible to know the size of angle $$c$$.

      Q4.
      An equilateral triangle has one side of length 40 cm. Which of these statements are correct?

      It is impossible to know any angles in this triangle, as none are given.
      Correct answer: All interior angles are 60°.
      Correct answer: A different side of this triangle has a length of 40 cm.
      A different side of this triangle has a length of 60 cm.
      Correct answer: The perimeter of the triangle is 120 cm.

      Q5.
      An isosceles triangle has an angle of 90°, and a side of length 19 cm. What is the size of one of its other angles, in degrees? °.

      Correct Answer: 45, 45°, 45 degrees, 45degrees

      Q6.
      Three different triangles each have an angle of 30°. Match the name of each triangle to their possible angles.

      Correct Answer:isosceles,another angle of 30° and one of 120°

      another angle of 30° and one of 120°

      Correct Answer:scalene,one angle of 77° and another 73°

      one angle of 77° and another 73°

      Correct Answer:right-angled scalene,an angle of 60° and one of 90°

      an angle of 60° and one of 90°

      Correct Answer:equilateral,impossible to have this triangle with an angle of 30°

      impossible to have this triangle with an angle of 30°


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