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Lesson 7 of 18

Congruent triangles (SSS)

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

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Lesson 7 of 18
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Congruent triangles (SSS)

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

Lesson details

Key learning points

  1. By knowing the three side lengths of the triangle and its image, you can prove congruence.
  2. The corresponding angle pairs will be the same.

Keywords

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

Common misconception

Pupils may believe that as the sides fix the angles, that this implies it is true conversely.

Use any regular polygon to highlight that the angles will always be the same, but the edge lengths are not always the same length. Regular polygons are always similar but not necessarily congruent.

Have your class, cut two identical sets of four strips of paper and label them a, b, c and d. Get them to investigate how they know for certain that two quadrilaterals are congruent to each other. They can then use only three to look at congruent triangles.
Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Prior knowledge starter quiz

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6 Questions

Q1.
In degrees, what is the size of the angle shown?

An image in a quiz
Correct Answer: 40, forty

Q2.
Select all the quadrilaterals that have at least one pair of equal sides.

Correct answer: Kite
Correct answer: Square
Trapezium
Irregular quadrilateral
Correct answer: Parallelogram

Q3.
These two rectangles are similar. This means that the side marked $$x$$ is cm.

An image in a quiz
Correct Answer: 4, four

Q4.
Quadrilaterals ABCD and HEFG are congruent. Match each side or angle in quadrilateral ABCD with a corresponding edge or angle in quadrilateral HEFG.

An image in a quiz
Correct Answer:AB,GF

GF

Correct Answer:CD,EH

EH

Correct Answer:BC,EF

EF

Correct Answer:∠DCB,∠FEH

∠FEH

Correct Answer:∠ADC,∠EHG

∠EHG

Correct Answer:∠DAB,∠HGF

∠HGF

Q5.
A transformation has taken place on a shape. The image is congruent to the object. Which transformation cannot have taken place?

translation
reflection
rotation
Correct answer: enlargement (SF$$\neq$$1)

Q6.
Match each quadrilateral with another quadrilateral that could have the same interior angles.

Correct Answer:Square,Rectangle

Rectangle

Correct Answer:Parallelogram,Rhombus

Rhombus

Correct Answer:Isosceles trapezium,Parallelogram

Parallelogram

Correct Answer:Kite,Trapezium

Trapezium

Assessment exit quiz

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6 Questions

Q1.
If triangle ABC is congruent to triangle PQR. Match the corresponding equal edges.

An image in a quiz
Correct Answer:AB,QR

QR

Correct Answer:BC,PR

PR

Correct Answer:AC,QP

QP

Q2.
Triangle MNO is congruent to triangle ABC by SSS and MN is 11 cm. Which angle in triangle MNO is opposite MN?

An image in a quiz
32°
45°
Correct answer: 103°

Q3.
Triangle MNO has two angles of 103° and 32°. Side MN is 12 cm. Are triangle ABC and MNO congruent?

An image in a quiz
Yes - their corresponding angles are the same.
Correct answer: No - the corresponding edges are not the same.

Q4.
STUV is a square. Match each statement to a reason to prove that triangle STU is congruent to triangle SVU by SSS.

Correct Answer:ST = SV,as ST and SV are both edges of the same square.

as ST and SV are both edges of the same square.

Correct Answer:TU = VU,as TU and VU are both edges of the same square.

as TU and VU are both edges of the same square.

Correct Answer:SU,is a common edge to both triangles.

is a common edge to both triangles.

Q5.
Jun measures each of these triangles. Which of the triangles are congruent to this triangle by SSS?

An image in a quiz
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

Q6.
PQRS is an isosceles trapezium. PR = QS. Match the letters in the proof with the correct edge.

An image in a quiz
Correct Answer:a,PQ

PQ

Correct Answer:b,QR

QR

Correct Answer:c,PR

PR

Lesson appears in

UnitMaths / Geometrical properties: similarity and Pythagoras' theorem

Maths

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