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Triangles for OCR GCSE Maths

Triangles

This page covers the following topics:

1. Sum of angles in a triangle
2. Isosceles, equilateral and scalene triangles
3. Right-angled, acute and obtuse triangles
4. 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

An equilateral triangle is one that has three equal sides and three equal angles. The angles of equilateral triangles are all 60ยบ. An isosceles triangle is one that has two equal sides and two equal angles. A scalene triangle is a triangle with no equal sides and no equal angles.

Isosceles, equilateral and scalene triangles

A right-angled triangle is one where one of the angles is 90ยบ. An obtuse triangle is one where one of the angles is more than 90ยบ. An acute triangle is one where all of the angles are less than 90ยบ.

Right-angled, acute and obtuse triangles

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

State if the given triangle is an obtuse or acute angle.

The given triangle is an isosceles triangle, therefore the two missing angles are equal.
So, 180 โˆ’ 48 = 132ยบ.
Therefore, the missing angles are 132/2 = 66ยบ.
So, all the angles in the triangle are less than 90ยบ, therefore the triangle is an acute one.

State if the given triangle is an obtuse or acute angle.

3

Find the missing value x and state what type of triangle is given in the diagram.

The triangle is an isosceles triangle, therefore the third angle in the triangle is also 72ยบ.
So, x = 180 โˆ’ (72 + 72) = 36ยบ.
Since all of the angles in the triangle are less than 90ยบ, therefore it is an acute triangle.

Find the missing value x and state what type of triangle is given in the diagram.

4

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.

5

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.

End of page

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