Year 6 - Maths
Two congruent triangles can be arranged to compose a parallelogram
Draw, compose and decompose shapes
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils will use knowledge of shape properties to draw, sketch and identify shapes.
Lesson Summary
You will learn to explain how two congruent triangles can arranged to compose a parallelogram.
Key Notes
- 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.
Vocabulary To Learn
- 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 Mistakes To Avoid
- 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.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
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.
2. Use this key word in a maths sentence and explain it clearly. 'Congruent'
If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: 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. Correction: 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.
More Lessons In This Unit
- 3D shapes can be composed from 2D nets Study Guide
- Any parallelogram can be decomposed and the parts rearranged to form a rectangular parallelogram Study Guide
- Reason about compound shapes using the relationship between side lengths and area and perimeter Study Guide
- Reason about shapes using the relationship between side lengths and area and perimeter Study Guide
- Shapes with the same areas can have different perimeters and vice versa Study Guide
- The same 3D shapes can be composed from different 2D nets Study Guide
- Use knowledge of shape properties to draw shapes accurately using rulers and protractors Study Guide
- Use knowledge of shape properties to sketch and identify shapes Study Guide
- When a 2D shape is decomposed and the parts rearranged, the areas remains the same Study Guide
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