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.

Pythagoras’ theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.

Checking and securing understanding of congruent triangles (RHS)

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

Pythagoras’ theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the {{}}.

The lengths of the 3 edges of some triangles are given. Select all the right-angled triangles.

A right-angled triangle has a hypotenuse of 17 m. Select the possible lengths of the two shorter sides.

Which of these pairs of triangles are congruent? 

Triangle ABC and triangle DEF are congruent and AB > BC. The length of the side $$x$$ is {{}} cm.

Match each letter which the correct statement to complete the proof that triangle DAC and triangle ABC are congruent.

…they are transformations of each other.

Two shapes will always be congruent if...

...they have 1 angles and 1 side that are the same.

...they have 2 angles and 1 side that are the same.

...two angles and one corresponding side are the same.

...two sides and the angle between them are the same.

Two triangles are guaranteed to be congruent if...

No, they are not congruent as the angles are in a different order.

No, they are not congruent as the 8.9 cm edges are not corresponding.

Are these two triangles congruent? Explain your answer.

These two triangles are congruent. Match each side length to its value.

Given these two triangles are congruent, the angle marked $$x$$ is {{}}°.

Opposite edges of a rhombus are parallel and equal. So, AD = BC 

So ∠ABD = ∠DBC as they are alternate angles in parallel lines

So ∠ADB = ∠DBC as they are alternate angles in parallel lines

∠BAD = ∠DBC (opposite angles are equal in rhombus) ∴ ABD and BCD congruent (ASA)

∠BAD = ∠BCD (opposite angles are equal in rhombus) ∴ ABD and BCD congruent (ASA)

ABCD is a rhombus. Select all the statements needed to show that triangles ABD and BCD are congruent using the ASA congruence condition. 

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