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
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In all right-angled triangles, what is true about the angles and ?-
- ✓
- ✓
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In this right-angled triangle, ______°- '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
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Exit quiz
- 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
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Triangle ABC and JKL are congruent by __________.- ASA
- RHS ✓
- SAS
- SSS
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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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Worksheet
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Presentation
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Video
Lesson Details
Key learning points
- 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.
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.
Keywords
Hypotenuse - The hypotenuse is the side of a right-angled triangle which is opposite the right angle.
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