Two congruent triangles can be arranged to compose a parallelogram | Maths

Starter quiz

Which of these are properties of all triangles?
- All sides must be equal.
- Four sides.
- Three interior angles. ✓
- 3-dimensional.
- All sides are straight. ✓
Match the triangle with the correct property.
- Equilateral
  
  ⇔
  
  Three equal sides. ✓
- Isosceles
  
  ⇔
  
  Two equal sides and one different. ✓
- Scalene
  
  ⇔
  
  No equal sides. ✓
- Right-angled
  
  ⇔
  
  One pair of perpendicular sides. ✓
Which of these polygons is also classified as a parallelogram?
- Triangle
- Square ✓
- Rectangle ✓
- Trapezium
Which of these statements apply to all parallelograms?
- Opposite angles are equal. ✓
- Opposite angles are different.
- Opposite sides are equal in length. ✓
- Opposite sides are different in length.
Which of these statements is true about these shapes?
- Both shapes are parallelograms. ✓
- Shape a is a parallelogram but Shape b is not.
- Neither shape is a parallelogram.
The two compound shapes have been composed of identical smaller shapes. Which of these statements is true?
- 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.
- They are both compound shapes. ✓

Exit quiz

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

Worksheet

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Lesson Details

Key learning points

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

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.

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.