A theorem that

Example: there is a

A

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

**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

Copyright © 2018 MathsIsFun.com