New
New
Year 8

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°.

New
New
Year 8

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°.

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Lesson details

Key learning points

  1. By considering a number of different triangles you can demonstrate facts about the angles in triangles.
  2. The interior angles of any triangle sum to 180°
  3. 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.

Have the pupils take part in the demonstration, by drawing a triangle, colouring the three angles and then tearing them off and arranging them at a point on a line. Discuss how they have not shown it works for all triangles, so it isn't a proof.
Teacher tip

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).

Lesson video

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6 Questions

Q1.
The value of $$a$$ is .
An image in a quiz
Correct Answer: 37, thirty seven, 37°
Q2.
Match the type of triangle and the description.
Correct Answer:scalene triangle,All three edges and angles are different to each other.

All three edges and angles are different to each other.

Correct Answer:isosceles triangle,At least two edges and two angles are equal to each other.

At least two edges and two angles are equal to each other.

Correct Answer:equilateral triangle,All three edges and angles are equal to each other.

All three edges and angles are equal to each other.

Correct Answer:right-angled triangle,One of the angles is 90°.

One of the angles is 90°.

Q3.
Which angles are always equal to the angle marked $$a$$?
An image in a quiz
$$b$$
Correct answer: $$c$$
$$d$$
Correct answer: $$e$$
$$f$$
Q4.
The value of the angle marked $$r$$° is °.
An image in a quiz
Correct Answer: 127, one hundred and twenty seven
Q5.
The value of the angle marked $$x$$° is °.
An image in a quiz
Correct Answer: 131, one hundred and thirty one
Q6.
The value of the angle marked $$m$$° is °.
An image in a quiz
Correct Answer: 116, one hundred and sixteen

6 Questions

Q1.
Select the statements that can correctly complete the following sentence. The angle marked $$g$$ ...
An image in a quiz
... is 52° because the angles on a line at a point sum to 180°.
Correct answer: ... 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°.
Correct answer: ... is 45° because the angles on a line at a point sum to 180°.
Q2.
The angles of any triangle sums to 180°.
Correct Answer: interior
Q3.
This diagram _________ that the angles in any triangle sum to 180°.
An image in a quiz
proves
Correct answer: demonstrates
Q4.
Which of the following could not be the angles in a triangle?
60°, 60° and 60°.
Correct answer: 92°, 104° and 14°.
50°, 60° and 70°.
24°, 24° and 132°.
Correct answer: 34°, 34° and 122°.
Q5.
Match each mathematical statement to the correct reasoning in this proof.
An image in a quiz
Correct Answer:∠OAB is equal to, ∠ABC as they are equal alternate angles

∠ABC as they are equal alternate angles

Correct Answer:∠DAC is equal to,∠ACB as they are equal alternate angles

∠ACB as they are equal alternate angles

Correct Answer:∠OAB + ∠BAC + ∠DAC = 180°,as angles on a line at a point sum to 180°

as angles on a line at a point sum to 180°

Correct Answer:∠ABC + ∠BAC + ∠ACB = 180°,as angles in a triangle sum to 180°

as angles in a triangle sum to 180°

Q6.
The size of the angle marked $$h$$° is °.
An image in a quiz
Correct Answer: 41, forty one, 41°