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- Year 9
Congruent triangles (SAS)
I can appreciate and use the criteria by which triangles are congruent (SAS).
- Year 9
Congruent triangles (SAS)
I can appreciate and use the criteria by which triangles are congruent (SAS).
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Lesson details
Key learning points
- By knowing two side lengths and the angle between them in the triangle and image, you can prove congruence.
- The angle between the sides must be the same in both object and image.
- 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.
To help you plan your year 9 maths lesson on: Congruent triangles (SAS), download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 9 maths lesson on: Congruent triangles (SAS), download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 3 maths lessons from the Geometrical properties: similarity and Pythagoras' theorem unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Prior knowledge starter quiz
6 Questions
Q1.The angle being measured is °.

Q2.The two marked angles are __________ angles in parallel lines.

Q3.Select all the properties of a parallelogram.
Q4.Rectangle A and rectangle B are similar. The length of the side marked $$x$$ is cm.

Q5.Triangle ABC and triangle XYZ are congruent. Which edge is 6.5 cm on triangle XYZ?

Q6.The diagram shows two pairs of lines intersecting at a point. The value of $$x$$ is .

Assessment exit quiz
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).
Q2.If triangles ABC and XYZ are congruent by SAS then is 9.6 cm.

Q3.Which of the following triangles have sufficient information to guarantee they are congruent to triangle ABC?





Q4.Which of the following triangles are congruent to triangle XYZ?





Q5.Are the triangles ABC and MNO congruent?

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.

∠BAF = ∠EFA -
as they are interior angles of a regular hexagon (= 120°)
∠GAF = ∠HFA -
as they are interior angles of a square (= 90°)
∠BAG = -
∠BAF − ∠GAF (= 30°)
∠HFE = -
∠EFA − ∠HFA (= 30°)
∠BAG = -
∠HFE
AB = AG = FH = FE -
as they are in regular polygons with shared edges