Basic Angle Properties (Cambridge (CIE) IGCSE International Maths): Revision Note

Basic angle properties

How do I label lines segments, angles and shapes?

• The line segment AB goes from point A to point B

• The angle ABC is formed by the line segments AB and BC

  • The angle is at point B

  • The angle is the acute or obtuse angle, not the reflex angle

• The triangle ABC is formed by the line segments AB, BC and CA

• The quadrilateral ABCD is formed by the line segments AB, BC, CD and DA

  • The points are labelled starting at a point and following the sides

  • ABDC is not the same shape because it is formed by the line segments AB, BD, DC and CA

• The same idea is used to label other polygons

What are the basic angle properties?

• Angles around a point add up to 360°

• Angles that form a straight line add up to 180°

• Vertically opposite angles are equal

  • Vertically opposite angles occur when two lines intersect, as in the diagram below

What are the angle properties of triangles?

• The three interior angles inside any triangle add up to 180°

• If the triangle is isosceles then two angles will be equal

  • These will be the two angles opposite the two sides of equal length

• If the triangle is equilateral then all three angles will be equal

  • Each angle will equal 60°

• A right-angled triangle has one 90° angle

What are the angle properties of quadrilaterals?

• The four interior angles inside any quadrilateral add up to 360°

• If the quadrilateral is a square or a rectangle then all the angles are equal to 90°

• You can use any symmetries of the quadrilateral to identify other equal angles

  • For a parallelogram (or rhombus), opposite angles are equal

  • For a kite, one pair of opposite angles are equal