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 (SAS)

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

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

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

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

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

Lucas: "No Jun, 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 are different.

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

Are triangle ABC and DEF congruent? Explain your answer.

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

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

AD = BC as the trapezium is symmetrical. AB is a common edge

AC = BD as the trapezium is symmetrical. AB is a common edge

Angle DAB = angle ABC as the trapezium is symmetrical.

∴ triangle ABC and triangle ABD are congruent by SAS.

∴ triangle ABC and triangle ABD are congruent by SSS.

ABCD is an isosceles trapezium. Select the statements needed to prove that triangle ABC and triangle ABD are congruent.

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

Which of these pairs of shapes are congruent to each other?

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

Alex: "All rhombi are similar to each other."

Jacob: "All isosceles triangles are similar to each other."

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

Sam: "All regular hexagons are similar to each other."

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

Andeep: "The angle marked $$w$$ is 53°."

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

AB = AD as they are opposite edges on a kite. Likewise BC = CD

AB = AD as they are adjacent edges on a kite. Likewise BC = CD

Angle ABC = Angle ACD as a kite has one pair of equal angles

∴ triangle ABC is congruent to triangle ADC by SSS.

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

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