1.3.4 Vertically opposite angles
When two straight lines cross, they form four angles. In the diagram below, these angles are labelled α, β, θ and φ and referred to as alpha, beta, theta and phi. The angles opposite each other are equal. They are called vertically opposite angles. Here α and β are a pair of vertically opposite angles, as are θ and φ. Although such angles are called ‘vertically opposite’, they do not need to be vertically above and below each other!
Activity 3: Vertically opposite angles
Clickfor Activity 3.
For two intersecting straight lines, vertically opposite angles are equal.
We can show that vertically opposite angles are equal as follows:
α and θ lie on a line.
So, α + θ = 180°
and α = 180° – θ
but β and θ also lie on a line.
So, β + θ = 180°
and β = 180° – θ.
Hence, α = β because they are both equal to 180° – θ.