Definition of


 vertically opposite angles
A theorem that follows on from another theorem.

Example: there is a Theorem that says: two angles that together form a straight line are "supplementary" (they add to 180°).

A Corollary to this is the "Vertical Angle Theorem" that says: where two lines intersect, the angles opposite each other are equal (a=c and b=d in the diagram).

Proof that a=c:
Angles a and b are on a straight line, so:
⇒ angles a + b = 180° and so a = 180° − b
Angles c and b are also on a straight line, so:
⇒ angles c + b = 180° and so c = 180° − b
So angle a = angle c
See: Theorem

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