Year 8 - Maths
The sum of the interior angles of any triangle
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 demonstrate and prove that in a triangle, the sum of the interior angles is 180°.
Key Notes
- By considering a number of different triangles you can demonstrate facts about the angles in triangles.
- The interior angles of any triangle sum to 180°
- The angle sum of triangles can be proved using angles in parallel lines.
Vocabulary To Learn
- Alternate angles: a pair of angles both between or both outside two line segments that are on opposite sides of the transversal that cuts them.
- Corresponding angles: Corresponding angles are a pair of angles at different vertices on the same side of a transversal in equivalent positions.
- Co-interior angles: Co-interior angles are on the same side of the transversal line and in between the two other lines.
Common Mistakes To Avoid
- Pupils may struggle with mathematical proof, especially using other knowledge within it.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
By considering a number of different triangles you can demonstrate facts about the angles in triangles. The interior angles of any triangle sum to 180°.
2. Use this key word in a maths sentence and explain it clearly. 'Alternate angles'
a pair of angles both between or both outside two line segments that are on opposite sides of the transversal that cuts them. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may struggle with mathematical proof, especially using other knowledge within it. Correction: Explain to pupils that there are many different styles of mathematical proof but all are showing that a particular fact holds true for all.
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
- Deriving the sum of interior angles in multiple ways 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
- Using the sum of the interior angles of a triangle Study Guide
Browse all guides in the Year 8 Maths guide library.