Question: how do you prove, without knowing any of the measurements or degrees, that the three angles of a triangle equal 180? what are the steps for proving that?

Hi Rachel,

Suppose the triangle has vertices ABC, then extend one side (I extended BC) to a point D. Next draw a line segment through C parallel to the opposite side (here AB).

Since AB and EC are parallel, and AC is a transversal, angle CAB is congruent to angle ACE.

Since AB and EC are parallel, and BC is a transversal, angle ABC is congruent to angle ECD.

Thus

angle BCA + angle CAB + angle ABC = angle BCA + angle ACE + angle ECD

But

angle BCA + angle ACE + angle ECD = angle BCD = 180^o

Thus

angle BCA + angle CAB + angle ABC = 180^o

Penny