Year 8 - Maths
Deriving the sum of interior angles in multiple ways
Geometrical properties: polygons
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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 investigate internal and external angles of polygons and angles made with a transveral and parallel lines. Pupils will develop their ability to formally prove properties of polygons to generalise.
Lesson Summary
You will learn to use reasoning to derive the sum of interior angles in multiple ways.
Key Notes
- Not all vertices of component shapes contribute to the sum of the interior angles of a composite shape.
- A numerical sequence can be used to derive the sum of interior angles.
- A formula can be derived to find the sum of interior angles.
Vocabulary To Learn
- Polygon: A polygon is a flat (2D), closed figure made up of straight line segments.
- Interior angle: An interior angle is an angle formed inside a polygon by two of its edges.
- Sum: The sum is the total when numbers are added together.
Common Mistakes To Avoid
- Interior angles always sum to 180 times the number of component triangles it is split into.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Not all vertices of component shapes contribute to the sum of the interior angles of a composite shape. A numerical sequence can be used to derive the sum of interior angles.
2. Use this key word in a maths sentence and explain it clearly. 'Polygon'
A polygon is a flat (2D), closed figure made up of straight line segments. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Interior angles always sum to 180 times the number of component triangles it is split into. Correction: If line segments drawn make new vertices in the polygon, its angles won't contribute to the sum of interior angles in the initial polygon.
More Lessons In This Unit
- Alternate angles Study Guide
- Angles on parallel lines traversed by a straight line Study Guide
- Checking understanding of angles from KS2 Study Guide
- Co-interior angles Study Guide
- Corresponding angles Study Guide
- Exterior angles of polygons Study Guide
- Formal angle notation Study Guide
- Formalising understanding of triangles from KS2 Study Guide
- Interior and exterior angles of regular polygons Study Guide
- Interior angles of a polygon Study Guide
- Missing angles Study Guide
- Problem solving with polygons Study Guide
- Securing understanding of angles from KS2 Study Guide
- The sum of the interior angles of any triangle Study Guide
- Using the sum of the interior angles of a triangle Study Guide
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