Angles in Triangles

1. 1 Draw three very different triangles on the board (right-angled, equilateral, scalene). 'What do you think is special about the angles in a triangle? Make a prediction.'
2. 2 Students tear off all three corners of their paper triangle. Arrange the three angles together at a point. 'What do you notice?' They should form a straight line — 180°. Students annotate: 'The angles in a triangle add up to 180°.'
3. 3 Students draw two new triangles and measure all three angles with a protractor. Add them up. 'Does it always give 180°? Even if your measurements are slightly off — why might that happen?'
4. 4 Model: 'A triangle has angles of 65° and 80°. What is the third?' Set up: 65 + 80 + ? = 180. So ? = 180 − 65 − 80 = 35°. Work through two more together.
5. 5 Equilateral: 'All three angles are equal — what is each one?' (60°). Isosceles: 'Two angles are equal. If one base angle is 70°, find the other two angles.' Students work these out.
6. 6 Students find missing angles in 6 triangles of varying types, including isosceles triangles where they must use both the angle sum and the equal-angle property.
7. 7 What is the maximum number of obtuse angles a triangle can have? (One.) Can a triangle have two right angles? Prove it using the angle sum rule.

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