The sum of the interior angles of any triangle | Maths

Starter quiz

The value of $a$ is ______.
- '37' ✓
Match the type of triangle and the description.
- 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°. ✓
Which angles are always equal to the angle marked $a$ ?
- $b$
- $c$ ✓
- $d$
- $e$ ✓
- $f$
The value of the angle marked $r$ ° is ______°.
- '127' ✓
The value of the angle marked $x$ ° is ______°.
- '131' ✓
The value of the angle marked $m$ ° is ______°.
- '116' ✓

Select the statements that can correctly complete the following sentence. The angle marked $g$ ...
- ... is 52° because the angles on a line at a point sum to 180°.
- ... is 45° because the angles in a triangle sum to 180°. ✓
- ... is 45° because it looks to be half of a right angle.
- ... is 52° as it is vertically opposite the 52°.
- ... is 45° because the angles on a line at a point sum to 180°. ✓
The ______ angles of any triangle sums to 180°.
- 'interior' ✓
This diagram _________ that the angles in any triangle sum to 180°.
- proves
- demonstrates ✓
Which of the following could not be the angles in a triangle?
- 60°, 60° and 60°.
- 92°, 104° and 14°. ✓
- 50°, 60° and 70°.
- 24°, 24° and 132°.
- 34°, 34° and 122°. ✓
Match each mathematical statement to the correct reasoning in this proof.
- ∠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° ✓
The size of the angle marked $h$ ° is ______°.
- '41' ✓

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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.

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.

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.