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

Starter quiz

Sofia says, "If one shape can fit exactly on top of another using reflection, __________ or __________, then the shapes are congruent." Select the words that correctly complete Sofia's statement.

enlargement

rotation ✓

similarity

transformation

translation ✓
Which of these pairs of shapes are congruent to each other?
Some Oak pupils are discussing congruence. Which pupils are correct?

Aisha: "All circles are similar to each other." ✓

Alex: "All rhombi are similar to each other."

Jacob: "All isosceles triangles are similar to each other."

Laura: "All pentagons are similar to each other."

Sam: "All regular hexagons are similar to each other." ✓
The diagram shows a pair of congruent triangles. The length of the side marked $y$ is ______ m.

'9' ✓
The diagram shows a pair of congruent triangles. Which of these Oak pupils are making a correct statement?

Alex: "The side marked $x$ is 108 mm." ✓

Andeep: "The angle marked $w$ is 53°."

Jacob: "The side marked $y$ is 66 mm." ✓

Lucas: "The side marked $z$ is 66 mm."

Sofia: "The angle $w$ ° is 95°." ✓
Select the statements needed to prove the following: "The diagonal of a kite bisects the shape into two congruent triangles."

AB = AD as they are opposite edges on a kite. Likewise BC = CD

AB = AD as they are adjacent edges on a kite. Likewise BC = CD ✓

Angle ABC = Angle ACD as a kite has one pair of equal angles

AC is a shared edge ✓

∴ triangle ABC is congruent to triangle ADC by SSS. ✓

Exit quiz

Jun says, "If one shape can fit exactly on top of another using rotation, __________ or __________ then the shapes are congruent." Select the words that correctly complete Jun's statement.

enlargement

reflection ✓

similarity

translation ✓

transformation
Some Oak pupils are discussing congruence. Which pupils are correct?

Andeep: "Two triangles are congruent if they have three edges the same." ✓

Izzy: "Two triangles are congruent if they have three angles the same."

Jun: "Two triangles are congruent if they have two edges and an angle the same."

Lucas: "No Jun, they must have two edges and the angle between them the same." ✓
Are triangle ABC and DEF congruent? Explain your answer.

No, the angles between the two equal sides are different. ✓

Yes, they have two equal sides, so the 3rd side is also fixed.

They are similar but not congruent.
Given these two triangles are congruent, find the length of the sides marked $x$ and $z$ .

Side $x$ is 8 cm ✓

Side $x$ is 15 cm

Side $x$ is 17 cm

Side $z$ is 15 cm

Side $z$ is 17 cm ✓
Given these two triangles are congruent, the angle marked $y$ is ______°.

'36' ✓
ABCD is an isosceles trapezium. Select the statements needed to prove that triangle ABC and triangle ABD are congruent.

AD = BC as the trapezium is symmetrical. AB is a common edge ✓

AC = BD as the trapezium is symmetrical. AB is a common edge

Angle DAB = angle ABC as the trapezium is symmetrical. ✓

∴ triangle ABC and triangle ABD are congruent by SAS. ✓

∴ triangle ABC and triangle ABD are congruent by SSS.

Worksheet

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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.

Common misconception

Pupils may try and use this criteria without knowing the angle between the two sides.

Pupils can construct triangles with two sides and an angle to see that there are two potential triangles, and therefore congruency is not guaranteed with SSA.

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.