Checking and securing understanding of congruent triangles (RHS) | Maths

Starter quiz

Two shapes will always be congruent if...

…they are enlargements of each other.

…they are rotations of each other. ✓

…they are similar to each other.

…they are translations of each other. ✓

…they are transformations of each other.
Two triangles are guaranteed to be congruent if...

...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.

...two angles and one corresponding side are the same. ✓

...two sides and the angle between them are the same. ✓
Are these two triangles congruent? Explain your answer.

No, they are not congruent as the angles are in a different order.

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.
These two triangles are congruent. Match each side length to its value.

$w$

⇔

14.2 cm ✓

$y$

⇔

16.3 cm ✓

$z$

⇔

11.8 cm ✓
Given these two triangles are congruent, the angle marked $x$ is ______°.

'42' ✓
ABCD is a rhombus. Select all the statements needed to show that triangles ABD and BCD are congruent using the ASA congruence condition.

Opposite edges of a rhombus are parallel and equal. So, AD = BC ✓

So ∠ABD = ∠DBC as they are alternate angles in parallel lines

So ∠ADB = ∠DBC as they are alternate angles in parallel lines ✓

∠BAD = ∠DBC (opposite angles are equal in rhombus) ∴ ABD and BCD congruent (ASA)

∠BAD = ∠BCD (opposite angles are equal in rhombus) ∴ ABD and BCD congruent (ASA) ✓

Exit quiz

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' ✓
The lengths of the 3 edges of some triangles are given. Select all the right-angled triangles.

6 cm, 8 cm, 10 cm ✓

7 cm, 9 cm, 11 cm

9 cm, 12 cm, 15 cm ✓

12 cm, 15 cm, 18 cm

15 cm, 20 cm, 25 cm ✓
A right-angled triangle has a hypotenuse of 17 m. Select the possible lengths of the two shorter sides.

7 m and 14 m

8 m and 15 m ✓

9 m and 13 m

10 m and 12 m
Which of these pairs of triangles are congruent?
Triangle ABC and triangle DEF are congruent and AB > BC. The length of the side $x$ is ______ cm.

'12' ✓
Match each letter which the correct statement to complete the proof that triangle DAC and triangle ABC are congruent.

a

⇔

90° ✓

b

⇔

AC ✓

c

⇔

BC ✓

d

⇔

RHS ✓

Worksheet

Loading worksheet ...

Presentation

Loading presentation ...

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 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.