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

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

Checking and securing understanding of congruent triangles (SSS)

Maths

In the prior unit, pupils enhanced their understanding of enlargement. In this unit, pupils investigate the effect of an enlargement on the perimeter and area of a 2-D shape and the volume of a 3-D shape.

Similarity

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. 

Which of these pairs of shapes look like they are congruent to each other?

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."

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

The diagram shows a pair of congruent triangles. The length of the side marked $$x$$ is {{ }} m.

Sam: "There is not enough information to find the angle $$w$$°."

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

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

∴ triangle ABD is congruent to triangle DBC by SSS.

Select the statements needed to prove the following: "The diagonal of a rhombus bisects the shape into two congruent triangles."

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

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

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.

A pentagon has a perimeter of 60 cm. The pentagon is enlarged by scale factor 5. The perimeter of the image is {{}} cm.

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

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.

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