Choose exam board for KS4 Computer Science (GCSE)
Choose exam board for KS4 English
Choose exam board for KS4 French
Choose exam board for KS4 Geography
Choose exam board for KS4 German
Choose exam board for KS4 History
Choose tier for KS4 Maths
Choose exam board for KS4 Music
Choose exam board for KS4 Physical education (GCSE)
Choose exam board for KS4 Religious education (GCSE)
Choose exam board for KS4 Spanish

      Lesson details

      Learning outcome

      I can appreciate and use the criteria by which triangles are congruent (RHS).

      Key learning points

      1. For a right-angled triangle, you need the hypotenuse and one other side length to prove congruence.
      2. Right-angled triangles, by definition, have a right-angle.
      3. There is a special relationship between the sides in a right-angled triangle.

      Keywords

      • Hypotenuse - The hypotenuse is the side of a right-angled triangle which is opposite the right angle.

      Common misconception

      Pupils may make assumptions about diagrams containing a right angle incorrectly.

      Remind pupils, that they cannot assume there is a right angle, just because it may look like the two edges are perpendicular to each other.

      Teacher tip

      You may wish to have students use a strip of paper (as a hypotenuse) and a corner of a desk to simulate the ladder scenario.

      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

      Loading...

      Prior knowledge starter quiz

      6 Questions

      Q1.
      Convert this measurement to centimetres: 23 mm = cm.

      Correct Answer: 2.3

      Q2.
      This angle is °.

      An image in a quiz
      Correct Answer: 45, forty five

      Q3.
      Which of these triangles can contain a right angle?

      Correct answer: scalene triangle
      Correct answer: isosceles triangle
      equilateral triangle
      obtuse-angled triangle

      Q4.
      In all right-angled triangles, what is true about the angles $$a°$$ and $$b°$$?

      An image in a quiz
      $$a°=b°$$
      Correct answer: $$a°+b°=90°$$
      $$a°<b°$$
      Correct answer: $$b°<90$$
      $$a°\ge90°$$

      Q5.
      In this right-angled triangle, $$a°=$$ °

      An image in a quiz
      Correct Answer: 28, twenty eight

      Q6.
      Select all the properties of a rhombus.

      Correct answer: All sides are equal
      Correct answer: Opposite angles are equal
      Diagonals are equal in length
      Correct answer: Diagonals are perpendicular
      No lines of symmetry

      6 Questions

      Q1.
      The hypotenuse is the side of a right-angle triangle which is the right angle.

      Correct Answer: opposite

      Q2.
      Which side in this triangle is the hypotenuse?

      An image in a quiz
      f
      Correct answer: g
      h

      Q3.
      Triangle ABC and JKL are congruent by __________.

      An image in a quiz
      ASA
      Correct answer: RHS
      SAS
      SSS

      Q4.
      Which of the these triangles are congruent to triangle ABC?

      An image in a quiz
      Correct Answer: 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

      Q5.
      Match each statement to a correct justification to prove that triangle PQS is congruent to triangle PRS by RHS.

      An image in a quiz
      Correct Answer:PQ = PR,given on the diagram. PQR is an isosceles triangle.
      Correct Answer:∠PSQ = ∠PSR = 90°,given on the diagram. PS is the altitude of the triangle.
      Correct Answer:PS,is a common edge to both triangles PQS and PRS

      Q6.
      Can triangles ABD and BCD ever be congruent?

      An image in a quiz
      Yes - they both share a side, they both have a right angle and one side is 2 cm
      Correct answer: No - the hypotenuse of one is a short side of another
      Not enough information - you do not know the other angles in the triangle

      To help you plan your 9 maths lesson on: Congruent triangles (RHS), download all teaching resources for free and adapt to suit your pupils' needs...