New
New
Year 9

Congruent triangles (SAS)

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

New
New
Year 9

Congruent triangles (SAS)

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

Lesson details

Key learning points

  1. By knowing two side lengths and the angle between them in the triangle and image, you can prove congruence.
  2. The angle between the sides must be the same in both object and image.
  3. The given sides must have the same multiplicative relationship.

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 the angle doesn't need to be in between the two known sides.

Use the Geogebra files to demonstrate that more than one triangle can be formed at times, and therefore it does not guarantee congruence between two triangles.

If pupils can have access to a computer, allow them to investigate and play with the different linked Geogebra files within this lesson.
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).

Lesson video

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6 Questions

Q1.
The angle being measured is °.
An image in a quiz
Correct Answer: 110, one hundred and ten
Q2.
The two marked angles are __________ angles in parallel lines.
An image in a quiz
exterior alternate
Correct answer: interior alternate
co-interior
corresponding
Q3.
Select all the properties of a parallelogram.
2 lines of symmetry
Correct answer: opposite angles are equal
Correct answer: opposite edges are equal
one set of parallel sides
Correct answer: four sets of supplementary co-interior angles
Q4.
Rectangle A and rectangle B are similar. The length of the side marked $$x$$ is cm.
An image in a quiz
Correct Answer: 12, twelve
Q5.
Triangle ABC and triangle XYZ are congruent. Which edge is 6.5 cm on triangle XYZ?
An image in a quiz
Correct answer: XY
XZ
YZ
Q6.
The diagram shows two pairs of lines intersecting at a point. The value of $$x$$ is .
An image in a quiz
Correct Answer: 60, sixty

6 Questions

Q1.
When there are two triangles, if the two corresponding edges and the angle between them are the same, you can prove they are congruent by (side-angle-side).
Correct Answer: SAS
Q2.
If triangles ABC and XYZ are congruent by SAS then is 9.6 cm.
An image in a quiz
Correct Answer: YZ, ZY
Q3.
Which of the following triangles have sufficient information to guarantee they 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
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
Q4.
Which of the following triangles are congruent to triangle XYZ?
An image in a quiz
Correct answer:
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
Q5.
Are the triangles ABC and MNO congruent?
An image in a quiz
Correct answer: Yes, they are guaranteed to be congruent.
No, they are definitely incongruent.
There is not enough information to tell.
Q6.
This diagram shows a regular hexagon ABCDEF and a square AGHF. Match the statements to prove triangle ABG and FHE are congruent by SAS.
An image in a quiz
Correct Answer:∠BAF = ∠EFA,as they are interior angles of a regular hexagon (= 120°)

as they are interior angles of a regular hexagon (= 120°)

Correct Answer:∠GAF = ∠HFA,as they are interior angles of a square (= 90°)

as they are interior angles of a square (= 90°)

Correct Answer:∠BAG = ,∠BAF − ∠GAF (= 30°)

∠BAF − ∠GAF (= 30°)

Correct Answer:∠HFE = ,∠EFA − ∠HFA (= 30°)

∠EFA − ∠HFA (= 30°)

Correct Answer:∠BAG = ,∠HFE

∠HFE

Correct Answer:AB = AG = FH = FE,as they are in regular polygons with shared edges

as they are in regular polygons with shared edges