Triangles for OCR GCSE Maths
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 180º. This property can be used to calculate missing angles in triangles.
An equilateral triangle is one that has three equal sides and three equal angles. The angles of equilateral triangles are all 60º. 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.
A right-angled triangle is one where one of the angles is 90º. An obtuse triangle is one where one of the angles is more than 90º. An acute triangle is one where all of the angles are less than 90º.
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.
State the sum of the angles in a triangle.
The sum of the angles in any triangle is 180º.
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 − 48 = 132º.
Therefore, the missing angles are 132/2 = 66º.
So, all the angles in the triangle are less than 90º, therefore the triangle is an acute one.
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 72º.
So, x = 180 − (72 + 72) = 36º.
Since all of the angles in the triangle are less than 90º, therefore it is an acute triangle.
Use the given diagram to calculate the value of x.
Using Pythagoras' Theorem, x² + (3x)² = 10², so 10x² = 100 and x² = 10 and x = √10.
Find the value of x in the given triangle.
The angle next to the 100º angle is given by 180 − 100 = 80º.
The second angle in the triangle is alternate angles with the 50º angle, therefore is equal to 50º.
So, x = 180 − (80 + 50) = 50º.
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