Congruent triangles (SAS) | Maths | Quizalize & Oak National Academy

Starter quiz

The angle being measured is ______°.

'110' ✓
The two marked angles are __________ angles in parallel lines.

exterior alternate

interior alternate ✓

co-interior

corresponding
Select all the properties of a parallelogram.

2 lines of symmetry

opposite angles are equal ✓

opposite edges are equal ✓

one set of parallel sides

four sets of supplementary co-interior angles ✓
Rectangle A and rectangle B are similar. The length of the side marked $x$ is ______cm.

'12' ✓
Triangle ABC and triangle XYZ are congruent. Which edge is 6.5 cm on triangle XYZ?

XY ✓

XZ

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

'60' ✓

Exit quiz

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).

'SAS' ✓
If triangles ABC and XYZ are congruent by SAS then ______ is 9.6 cm.

'YZ' ✓
Which of the following triangles have sufficient information to guarantee they are congruent to triangle ABC?
Which of the following triangles are congruent to triangle XYZ?

✓
Are the triangles ABC and MNO congruent?

Yes, they are guaranteed to be congruent. ✓

No, they are definitely incongruent.

There is not enough information to tell.
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 ✓

Worksheet

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Video

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.

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.

Keywords

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