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Year 6

Two congruent triangles can be arranged to compose a parallelogram

I can explain how two congruent triangles can arranged to compose a parallelogram.

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Year 6

Two congruent triangles can be arranged to compose a parallelogram

I can explain how two congruent triangles can arranged to compose a parallelogram.

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Lesson details

Key learning points

  1. The area of a triangle is equal to half the area of the parallelogram you create from 2 congruent triangles.
  2. Any parallelogram can be decomposed into two congruent triangles.

Keywords

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

  • Parallelogram - A parallelogram is a quadrilateral with two pairs of parallel and equal sides.

Common misconception

If pupils do not cut a parallelogram from vertex to opposite vertex, they will end up with either two non-congruent shapes or two congruent quadrilaterals.

Modelling is key and this is a useful time to revisit the concept of a shape's diagonal, that is, a line connecting vertex to a non-adjacent vertex.

In this lesson pupils will need to be familiar with triangle types and their properties. Consider how you might scaffold this knowledge for learners if required.
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This content is © Oak National Academy Limited (2025), licensed on
Open Government Licence version 3.0
except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Which of these are properties of all triangles?
All sides must be equal.
Four sides.
Correct answer: Three interior angles.
3-dimensional.
Correct answer: All sides are straight.
Q2.
Match the triangle with the correct property.
Correct Answer:Equilateral,Three equal sides.
tick

Three equal sides.

Correct Answer:Isosceles,Two equal sides and one different.
tick

Two equal sides and one different.

Correct Answer:Scalene,No equal sides.
tick

No equal sides.

Correct Answer:Right-angled,One pair of perpendicular sides.
tick

One pair of perpendicular sides.

Q3.
Which of these polygons is also classified as a parallelogram?
Triangle
Correct answer: Square
Correct answer: Rectangle
Trapezium
Q4.
Which of these statements apply to all parallelograms?
Correct answer: Opposite angles are equal.
Opposite angles are different.
Correct answer: Opposite sides are equal in length.
Opposite sides are different in length.
Q5.
Which of these statements is true about these shapes?
An image in a quiz
Correct answer: Both shapes are parallelograms.
Shape a is a parallelogram but Shape b is not.
Neither shape is a parallelogram.
Q6.
The two compound shapes have been composed of identical smaller shapes. Which of these statements is true?
An image in a quiz
Correct answer: The shapes have the same area.
The area of a is greater than the area of b.
The area of b is greater than the area of a.
Correct answer: They are both compound shapes.

Exit quiz

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6 Questions

Q1.
If two shapes are congruent, what does this mean?
Correct answer: They are the same type of shape.
They are different types of shape.
Correct answer: They are the same size.
They are different sizes.
Q2.
Which of these triangles are congruent?
An image in a quiz
Correct answer: a
b
Correct answer: c
d
Q3.
Which of these statements could be true of two congruent shapes?
Correct answer: They could be the same shape but rotated.
Correct answer: They could be the same shape but reflected.
They must be identical in every way including their position.
Q4.
Which of the statements are true?
A triangle can be composed from two parallelograms.
Correct answer: A parallelogram can be composed from two congruent triangles.
Correct answer: A parallelogram can be decomposed into two congruent triangles.
Q5.
This parallelogram has been decomposed into two congruent triangles. What type of triangle is each part?
An image in a quiz
equilateral
isosceles
Correct answer: scalene
Q6.
Which of these quadrilaterals cannot be decomposed into two congruent triangles?
Parallelogram
Rectangle
Square
Rhombus
Correct answer: Trapezium