IGCSE Maths / Working with shape and space
Angles in special triangles
Edexcel International GCSE Maths (4MA1), chapter 11: Working with shape and space, specification point 4.1d. Free lesson.
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Special triangles have angle properties you can use to find missing angles. Recognising the diagram marks and giving the correct reason helps you earn the method marks.
What the triangle marks tell you
The marks show which sides or angles are equal. The position of a triangle on the page does not change its properties, so read the marks rather than relying on its orientation. An isosceles triangle has two sides the same length, so the two angles opposite those sides are equal. These are called the base angles. An equilateral triangle has three equal sides and three angles of 60°. A right-angled triangle has one angle of 90°. Its sides are not fixed by this fact. Matching dashes show equal sides. A small square marks a right angle.
How to find the base angles in an isosceles triangle
The angles in any triangle add up to 180°. If the angle between the two equal sides is given, subtract it from 180° first. The remaining amount belongs to the two equal base angles, so divide it by 2. The reason to state is: base angles of an isosceles triangle are equal.
How to combine the isosceles rule with a straight line
Sometimes finding a base angle is only the first step. Use one rule at a time, and give a reason for each step. Angles on a straight line add up to 180°. When two different angles meet at the same point, use three letters to identify each one precisely.
How equilateral and isosceles triangles are related
Every equilateral triangle is also isosceles: three equal sides include at least two equal sides. Its three 60° angles also include two equal angles. The reverse is not always true, because an isosceles triangle does not need to have all three sides equal.
More lessons in Working with shape and space
- Angles at a point and on a line
- Angles in parallel lines
- Angle sum of a triangle
- Exterior angle of a triangle
- Angle sum of a quadrilateral
- Properties of quadrilaterals
- Writing geometrical reasons
- Angle sum of a polygon
- Interior and exterior angles of regular polygons
- Finding the number of sides from an angle
- Irregular polygon angle problems
- Perimeter and area of rectangles and triangles
- Area of a parallelogram
- Area of a trapezium
- Names of solids: faces, edges and vertices
- Surface area of a cuboid
- Surface area of a triangular prism
- Volume of a prism
- Compound prisms and volume units
- Time intervals, money and currency
- Converting units of length, area and volume