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      Constructing a triangle given two angles and the side length between them

      Lesson details

      Learning outcome

      I can construct a triangle given two angles and the side length between them.

      Key learning points

      1. The side can be drawn accurately with a ruler
      2. Both angles should be accurately measured with a protractor
      3. Where the lines marking each angle intersect is where the lines should be drawn to
      4. All triangles with the same measurements are congruent

      Keywords

      • Congruent - If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.

      Common misconception

      Pupils may struggle to spot congruent triangles if they only look for ASA (angle-side-angle).

      Encourage pupils to add any further information to diagrams, like the third angle, before starting to prove congruence.

      Teacher tip

      Pupils can calculate the third angle and use a protractor to check the accuracy of their constructions.

      Equipment

      Pair of compasses, protractor and ruler

      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 diagram shows part of a protractor measuring an angle. What is the size of the angle?

      An image in a quiz
      Correct answer: 72°
      88°
      108°
      112°

      Q2.
      The diagram shows a protractor measuring an angle. What is the size of the angle?

      An image in a quiz
      56°
      64°
      Correct answer: 124°
      136°

      Q3.
      Jacob is using GeoGebra to accurately draw a triangle with side lengths 8 units, 9 units and an angle of size 67° between them. Which tool should Jacob use to construct a ray line?

      An image in a quiz
      a
      b
      c
      Correct answer: d

      Q4.
      A pair of compasses is used to draw an arc. The value of $$x$$ is .

      An image in a quiz
      Correct Answer: 11

      Q5.
      Laura draws a ray line and a circle with radius 10 units then marks their intersection with point C. Which line segment has a length of 10 units?

      An image in a quiz
      Correct Answer: AC, CA

      Q6.
      Match each step to the correct instruction needed to construct triangle ABC.

      An image in a quiz
      Correct Answer:Step 1,Use a ruler to draw side AC of 7 cm.

      Use a ruler to draw side AC of 7 cm.

      Correct Answer:Step 2,Use a protractor to measure 52° at A and mark a faint point.

      Use a protractor to measure 52° at A and mark a faint point.

      Correct Answer:Step 3,Draw a ray line through A to show direction of AB.

      Draw a ray line through A to show direction of AB.

      Correct Answer:Step 4,Set compasses to width of 9 cm and mark an arc on the ray.

      Set compasses to width of 9 cm and mark an arc on the ray.

      Correct Answer:Step 5,Label point where arc meets the ray as B.

      Label point where arc meets the ray as B.

      Correct Answer:Step 6,Use a ruler to connect C and B.

      Use a ruler to connect C and B.

      6 Questions

      Q1.
      What equipment should you use to make an accurate construction of this triangle?

      An image in a quiz
      a pair of compasses
      Correct answer: a protractor
      a rubber to rub out all construction lines
      Correct answer: a ruler
      Correct answer: a sharp pencil

      Q2.
      The diagram shows part of a protractor measuring an angle. What is the size of the angle?

      An image in a quiz
      Correct answer: 78°
      82°
      102°
      118°

      Q3.
      The diagram shows part of a protractor measuring an angle. What is the size of the angle?

      An image in a quiz
      Correct answer: 15°
      25°
      165°
      175°

      Q4.
      Laura is using GeoGebra to accurately draw a triangle with ∠BAC = 125° and ∠ABC = 32° and side AB = 5 units. Which tool should Laura use to plot point C?

      An image in a quiz
      a
      b
      Correct answer: c
      d

      Q5.
      ∠ABC = °.

      An image in a quiz
      Correct Answer: 76

      Q6.
      Match each step to the correct instruction needed to construct triangle ABC.

      An image in a quiz
      1 - Use a ruler to draw side AB of 7 cm.
      2 - Use a protractor to measure 38° from A and mark a faint point.
      3 - Repeat the last step with point B and an angle of 43°.
      4 - Draw a ray line to show direction of side AC.
      5 - Draw a second ray line to show direction of side BC.
      6 - Label point C at the point where the two rays meet.

      To help you plan your 11 maths lesson on: Constructing a triangle given two angles and the side length between them, download all teaching resources for free and adapt to suit your pupils' needs...