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°.
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.
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.
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.
Licence
This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
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°
