New
New
Year 10
Higher

Checking and securing understanding of congruent triangles (RHS)

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

New
New
Year 10
Higher

Checking and securing understanding of congruent triangles (RHS)

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

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 incorrect assumptions about diagrams containing a right angle.

Remind pupils that they cannot assume there is a right angle, just because two line segments look as if they are perpendicular to each other.

Keywords

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

  • Similar - Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions.

  • Pythagoras' theorem - Pythagoras’ theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.

If your pupils need further support or practice, consider the unit Geometrical properties: similarity and Pythagoras' theorem. Pupils working on the higher tier may want to concentrate their time on the second learning cycle.
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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6 Questions

Q1.
Two shapes will always be congruent if...
…they are enlargements of each other.
Correct answer: …they are rotations of each other.
…they are similar to each other.
Correct answer: …they are translations of each other.
…they are transformations of each other.
Q2.
Two triangles are guaranteed to be congruent if...
Correct answer: ...they have 3 sides that are the same.
...they have 1 angles and 1 side that are the same.
...they have 2 angles and 1 side that are the same.
Correct answer: ...two angles and one corresponding side are the same.
Correct answer: ...two sides and the angle between them are the same.
Q3.
Are these two triangles congruent? Explain your answer.
An image in a quiz
No, they are not congruent as the angles are in a different order.
Correct answer: No, they are not congruent as the 8.9 cm edges are not corresponding.
Yes, they are congruent by SAS.
Yes, they are congruent by ASA.
Q4.
These two triangles are congruent. Match each side length to its value.
An image in a quiz
Correct Answer:$$w$$,14.2 cm

14.2 cm

Correct Answer:$$y$$,16.3 cm

16.3 cm

Correct Answer:$$z$$,11.8 cm

11.8 cm

Q5.
Given these two triangles are congruent, the angle marked $$x$$ is °.
An image in a quiz
Correct Answer: 42
Q6.
ABCD is a rhombus. Select all the statements needed to show that triangles ABD and BCD are congruent using the ASA congruence condition.
An image in a quiz
Correct answer: Opposite edges of a rhombus are parallel and equal. So, AD = BC
So ∠ABD = ∠DBC as they are alternate angles in parallel lines
Correct answer: So ∠ADB = ∠DBC as they are alternate angles in parallel lines
∠BAD = ∠DBC (opposite angles are equal in rhombus) ∴ ABD and BCD congruent (ASA)
Correct answer: ∠BAD = ∠BCD (opposite angles are equal in rhombus) ∴ ABD and BCD congruent (ASA)

6 Questions

Q1.
Pythagoras’ theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the .
Correct Answer: hypotenuse
Q2.
The lengths of the 3 edges of some triangles are given. Select all the right-angled triangles.
Correct answer: 6 cm, 8 cm, 10 cm
7 cm, 9 cm, 11 cm
Correct answer: 9 cm, 12 cm, 15 cm
12 cm, 15 cm, 18 cm
Correct answer: 15 cm, 20 cm, 25 cm
Q3.
A right-angled triangle has a hypotenuse of 17 m. Select the possible lengths of the two shorter sides.
7 m and 14 m
Correct answer: 8 m and 15 m
9 m and 13 m
10 m and 12 m
Q4.
Which of these pairs of triangles are congruent?
Correct Answer: An image in a quiz
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.
Triangle ABC and triangle DEF are congruent and AB > BC. The length of the side $$x$$ is cm.
An image in a quiz
Correct Answer: 12
Q6.
Match each letter which the correct statement to complete the proof that triangle DAC and triangle ABC are congruent.
An image in a quiz
Correct Answer:a,90°

90°

Correct Answer:b,AC

AC

Correct Answer:c,BC

BC

Correct Answer:d,RHS

RHS