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 (ASA)

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

…they are transformations of each other.

Two shapes will always be congruent if...

...they have any 2 angles that are the same .

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

Two triangles are guaranteed to be congruent if...

No, they are not congruent as the 7.3 cm edges are not corresponding.

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

Are these two triangle 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 {{}}°.

As NQ = QO, then triangle NQO is an equilateral triangle. Hence ∠QNO = ∠QON

As NQ = QO, then triangle NQO is an isosceles triangle. Hence ∠QNO = ∠QON

NP is a shared edge. ∠MNO = ∠PON as given.

NO is a shared edge. ∠MNO = ∠PON as given.

∴ triangle MNO is congruent to triangle PNO by ASA.

In the diagram, ∠MNO = ∠PON and NQ = QO. Select the statements that are needed to prove that triangle MNO is congruent to triangle PNO. 

Izzy says, "__________ shapes can fit exactly on top of another using rotation, __________ or __________ ." Select the words that correctly complete Izzy's statement.

Andeep: Two triangles are congruent if they both have a right-angle.

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

Jacob: Two triangles are congruent if they have three edges the same.

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

Laura: "No, they must have two edges and the angle between them the same."

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

No, the angles between the two equal sides is different.

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

Yes, the angles between the two equal sides are the same.

Are triangle ABC and DEF congruent? Explain your answer.

Given these two triangles are congruent, find the length of the sides marked $$x$$ and $$y$$.

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

AD = BC as the shape is a rhombus. Also, AB = CD

Angle ADC = angle ABC as opposite angles in a rhombus are equal.

Angle BAD = angle BCD as opposite angles in a rhombus are equal.

∴ triangle ABD and triangle BCD are congruent by SAS.

ABCD is a rhombus. Select the set of statements needed to prove that triangle ABD and triangle BCD are congruent.

Starter Quiz