Checking and securing understanding of congruence and similarity | Maths

Starter quiz

A property of a shape is __________ if that property has not changed after the shape is transformed.

congruent

invariant ✓

similar

translated
When an object is transformed the resulting shape is called the ______.

'image' ✓
The size of the missing angle in this quadrilateral is ______°.

'107' ✓
Select the transformations that will always produce an image that is congruent to the object.

enlargement

reflection ✓

rotation ✓

translation ✓
What are the lengths of the sides that are adjacent to the angle of 80° in this quadrilateral?

9 cm ✓

10 cm

17 cm ✓

18 cm
Rectangle B is an enlargement of rectangle A by scale factor 2. Rectangle A has perimeter = 16 cm and area = 15 cm². Both rectangles have integer side lengths. Find the area and perimeter of B.

Area = 30 cm²

Area = 60 cm² ✓

Perimeter = 32 cm ✓

Perimeter = 64 cm

Two shapes are ______ if the only difference between them is their size. Their side lengths are in the same proportions.

'similar' ✓
If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are ______.

'congruent' ✓
Select the transformations that will always produce an image that is congruent to the object.

enlargement

reflection ✓

rotation ✓

translation ✓
Some Oak pupils discuss whether shapes A and B are congruent or similar. Who is correct?

Andeep: "The shapes are congruent because they have the same angles."

Jacob: "The shapes could be congruent but we need the other sides for shape B."

Laura: "The shapes could be similar but we need the other sides for shape B."

Sam: "Both shapes have the same corresponding side labelled 9 cm."

Sofia: "They have the same angles, but not side lengths so they are similar." ✓
Shapes A and B are congruent. What is the length of the side marked $x$ ?

11 cm

15 cm

18 cm ✓
Quadrilaterals A and B are similar. The length of the side marked $x$ is ______ cm.

'20' ✓

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If two shapes are congruent, then they are similar.
A ratio table can be a helpful tool for checking the multipliers.
The multiplicative relationship between the sides of the object is preserved in its image.
It can be easier to determine (by eye) which shapes are NOT congruent or similar.

Congruent shapes are not similar shapes.

Congruent shapes are similar shapes. The scale factor, or multiplier, between them is one.

Similar - Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions.
Congruent - If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.
Object - The object is the starting figure, before a transformation has been applied.
Image - The image is the resulting figure, after a transformation has been applied.
Invariant - A property of a shape is invariant if that property has not changed after the shape is transformed.