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Year 9

Congruent triangles (RHS)

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

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New
New
Year 9

Congruent triangles (RHS)

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

Download all resources
Share activities with pupils

Lesson details

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.

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.

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.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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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 $$b°$$?
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$$a°=b°$$
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

Exit quiz

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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.
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Correct Answer:PQ = PR,given on the diagram. PQR is an isosceles triangle.

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.

given on the diagram. PS is the altitude of the triangle.

Correct Answer:PS,is a common edge to both triangles PQS and PRS

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