ANGLES IN A TRIANGLE
You probably know that the three angles in a triangle add up to 180 .
But do you know why? In fact, it is very easy to see.
The following proof is based on the idea of alternate angles.
In the diagram on the left, the two angles in the
“armpits” of the Z shape are equal. This is true if and
only if the two horizontal lines are parallel.
So how do we know that the three angles of a triangle add up to 180 ?
The secret is to construct a line through the top vertex of the triangle, and
parallel to the base:
We now know some equal pairs of angles:
The angles marked a are equal, because
they are alternate angles.
The same goes for the angles marked b.
Therefore, looking at the top of the
diagram, a + b + c = 180 , because
angles on a straight line sum to 180.
Therefore, the three angles of the triangle, also a, b and c, add up to 180.