Congruent triangles (RHS) | Maths | Quizalize & Oak National Academy

Starter quiz

Convert this measurement to centimetres: 23 mm = ______ cm.
- '2.3' ✓
This angle is ______°.
- '45' ✓
Which of these triangles can contain a right angle?
- scalene triangle ✓
- isosceles triangle ✓
- equilateral triangle
- obtuse-angled triangle
In all right-angled triangles, what is true about the angles $a°$ and $b°$ ?
- $a°=b°$
- $a°+b°=90°$ ✓
- $a°$
- $b°<90$ ✓
- $a°\ge90°$
In this right-angled triangle, $a°=$ ______°
- '28' ✓
Select all the properties of a rhombus.
- All sides are equal ✓
- Opposite angles are equal ✓
- Diagonals are equal in length
- Diagonals are perpendicular ✓
- No lines of symmetry

The hypotenuse is the side of a right-angle triangle which is ______ the right angle.
- 'opposite' ✓
Which side in this triangle is the hypotenuse?
- f
- g ✓
- h
Triangle ABC and JKL are congruent by __________.
- ASA
- RHS ✓
- SAS
- SSS
Which of the these triangles are congruent to triangle ABC?
Match each statement to a correct justification to prove that triangle PQS is congruent to triangle PRS by RHS.
- PQ = PR
  
  ⇔
  
  given on the diagram. PQR is an isosceles triangle. ✓
- ∠PSQ = ∠PSR = 90°
  
  ⇔
  
  given on the diagram. PS is the altitude of the triangle. ✓
- PS
  
  ⇔
  
  is a common edge to both triangles PQS and PRS ✓
Can triangles ABD and BCD ever be congruent?
- Yes - they both share a side, they both have a right angle and one side is 2 cm
- No - the hypotenuse of one is a short side of another ✓
- Not enough information - you do not know the other angles in the triangle

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

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.

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