The sum of the interior angles of any triangle
I can demonstrate and prove that in a triangle, the sum of the interior angles is 180°.
The sum of the interior angles of any triangle
I can demonstrate and prove that in a triangle, the sum of the interior angles is 180°.
These resources will be removed by end of Summer Term 2025.
Lesson details
Key learning points
- 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.
Keywords
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 misconception
Pupils may struggle with mathematical proof, especially using other knowledge within it.
Explain to pupils that there are many different styles of mathematical proof but all are showing that a particular fact holds true for all.
To help you plan your year 8 maths lesson on: The sum of the interior angles of any triangle, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 8 maths lesson on: The sum of the interior angles of any triangle, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 3 maths lessons from the Geometrical properties: polygons unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
Licence
Lesson video
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Starter quiz
6 Questions
scalene triangle -
All three edges and angles are different to each other.
isosceles triangle -
At least two edges and two angles are equal to each other.
equilateral triangle -
All three edges and angles are equal to each other.
right-angled triangle -
One of the angles is 90°.
Exit quiz
6 Questions
∠OAB is equal to -
∠ABC as they are equal alternate angles
∠DAC is equal to -
∠ACB as they are equal alternate angles
∠OAB + ∠BAC + ∠DAC = 180° -
as angles on a line at a point sum to 180°
∠ABC + ∠BAC + ∠ACB = 180° -
as angles in a triangle sum to 180°
