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Triangles for SQA National 5 Maths

Triangles

This page covers the following topics:

1. Sum of angles in a triangle
2. Pythagoras' theorem

The sum of the angles in any triangle is 180ยบ. This property can be used to calculate missing angles in triangles.

Sum of angles in a triangle

The hypotenuse of a right-angled triangle is its longest side and is always opposite the right angle. The square of the hypotenuse can be found by adding the squares of the other two sides of the triangle.

Pythagoras' theorem

1

State the sum of the angles in a triangle.

The sum of the angles in any triangle is 180ยบ.

State the sum of the angles in a triangle.

2

Use the given diagram to calculate the value of x.

Using Pythagoras' Theorem, xยฒ + (3x)ยฒ = 10ยฒ, so 10xยฒ = 100 and xยฒ = 10 and x = โˆš10.

Use the given diagram to calculate the value of x.

3

Find the value of x in the given triangle.

The angle next to the 100ยบ angle is given by 180 โˆ’ 100 = 80ยบ.
The second angle in the triangle is alternate angles with the 50ยบ angle, therefore is equal to 50ยบ.
So, x = 180 โˆ’ (80 + 50) = 50ยบ.

Find the value of x in the given triangle.

4

Calculate the value of x.

Using Pythagoras' Theorem, xยฒ + 20ยฒ = 25ยฒ, so xยฒ = 225 and x = 15.

Calculate the value of x.

5

Use the given triangle to show that the angles in a triangle add up to 180ยบ.

The angles vertically opposite the two 60ยบ angles are also 60ยบ.
The angle next to the 120ยบ angle is 180 โˆ’ 120 = 60ยบ.
So, sum of angles = 60 + 60 + 60 = 180ยบ.

Use the given triangle to show that the angles in a triangle add up to 180ยบ.

End of page

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