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      Lesson details

      Learning outcome

      I can recognise that a pair of parallel lines traversed by a straight line produces equal alternate angles.

      Key learning points

      1. Alternate angles can be identified in an arrangement of 3 line segments.
      2. If two of the lines are parallel these alternate angles are equal.
      3. Knowledge of alternate angles can be used to find unknown angles.
      4. Knowledge of corresponding and alternate angles can be used to find unknown angles.

      Keywords

      • Alternate angles - A pair of angles both between or both outside two line segments that are on opposite sides of the transversal that cuts them.

      Common misconception

      Referring to alternate angles as 'Z' angles because of the arrangement of the lines.

      Modelling the justification correctly through every example and using exterior alternate angles to highlight the limitations of 'Z' angles.

      Teacher tip

      If available, use mini-whiteboards and ask the students to draw a diagram that shows "exterior alternate angles", "interior alternate angles", "equal interior alternate angles" etc.

      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.
      The size of the angle marked $$a$$ is °.

      An image in a quiz
      Correct Answer: 56, fifty six, 56°

      Q2.
      The value of the angle marked $$x$$ is °.

      An image in a quiz
      Correct Answer: 88, eighty eight, 88°

      Q3.
      Work out the value of $$m$$.

      An image in a quiz
      20
      Correct answer: 107
      127
      160

      Q4.
      Which pair of line segments are parallel to each other in this diagram?

      An image in a quiz
      AE
      Correct answer: BF
      IJ
      Correct answer: CG
      AB

      Q5.
      A transversal is any line that two or more lines at distinct (different) points.

      Correct Answer: intersects

      Q6.
      Which of the following show a pair of corresponding angles?

      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

      6 Questions

      Q1.
      Alternate angles are a pair of angles both between or both outside two line segments that are on sides of the transversal that cuts them.

      Correct Answer: opposite

      Q2.
      Which of these diagrams show a pair of alternate angles?

      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

      Q3.
      This diagram shows a pair of equal alternate angles.

      An image in a quiz
      Correct Answer: exterior

      Q4.
      Select the correct justification for the statement. The angle marked $$m$$ is 118°.

      An image in a quiz
      Because it is an interior alternate angle with the given angle.
      Because it is an exterior alternate angle with the given angle.
      Correct answer: Because it is an equal interior alternate angle with the given angle.
      Because it is an equal exterior alternate angle with the given angle.

      Q5.
      If alternate angles are equal, then the two lines are __________.

      Correct answer: parallel
      perpendicular
      the same length
      different

      Q6.
      Use this diagram to match each angle to an equal alternate angle.

      An image in a quiz
      Correct Answer:a,g
      Correct Answer:b,h
      Correct Answer:c,e
      Correct Answer:d,f

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