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

Starter quiz

__________ is the multiplier between similar shapes that describes how large one shape is compared to the other.

An enlargement factor

A ratio

A scale factor ✓

A vector
$This sector is enlarged by scale factor <Math>\frac{1}{3}</Math>. The angle in the image is <span class="blank">______</span>°.$

This sector is enlarged by scale factor $\frac{1}{3}$ . The angle in the image is ______°.

'60' ✓
Each square on this coordinate grid is 1 unit long. This object is enlarged by a scale factor of 3 to make its image. The perimeter of the image is ______ cm.

'11' ✓
A pentagon has a perimeter of 60 cm. The pentagon is enlarged by scale factor 5. The perimeter of the image is ______ cm.

'300' ✓
$The object is enlarged by a scale factor of <Math>\frac{1}{4}</Math> to make the image. What is the perimeter of the image?$

The object is enlarged by a scale factor of $\frac{1}{4}$ to make the image. What is the perimeter of the image?

8.25 cm

11 cm

12.5 cm

16.5 cm ✓
A shape is enlarged by a scale factor of $\frac{2}{5}$ to make its image. The perimeter of the image is 28 cm. The perimeter of the object is ______ cm.

'70' ✓

Exit quiz

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

enlargement

reflection ✓

rotation ✓

similarity

transformation
Which of these pairs of shapes look like they are congruent to each other?
Some Oak pupils are discussing congruence. Which pupils are correct?

Aisha: "All rectangles are similar to each other."

Andeep: "All squares are similar to each other." ✓

Jun: "All equilateral triangles are similar to each other." ✓

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

Sofia: "All circles are similar to each other." ✓
The diagram shows a pair of congruent triangles. The length of the side marked $x$ is ______ m.

'7' ✓
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." ✓

Aisha: "The angle marked $w$ is 53°."

Lucas: "The side marked $y$ is 85 mm."

Sofia: "The side marked $z$ is 85 mm." ✓

Sam: "There is not enough information to find the angle $w$ °."
Select the statements needed to prove the following: "The diagonal of a rhombus bisects the shape into two congruent triangles."

AC = BC = CD = DA as they are edges of a rhombus. ✓

AC = BD as the shape is a rhombus.

AC is a shared edge.

BD is a shared edge. ✓

∴ triangle ABD is congruent to triangle DBC by SSS. ✓

Worksheet

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Video

Lesson Details

Key learning points

By knowing the three side lengths of the triangle and its image, you can prove congruence.
If congruent, the same multiplicative relationship will exist for each pair of side lengths.
The angle pairs will be the same.

Common misconception

Pupils may believe that knowing the three angles is sufficient to prove two triangles are congruent.

Use an equilateral triangle to show that, although two equilateral triangles have the same angles, they are not guaranteed to be congruent. In fact they are similar.

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.