Question

Prove that the sum of the angles of a triangle is 180​

Answer 1

Answer:

Theorem

If ABC is a triangle then <)ABC + <)BCA + <)CAB = 180 degrees.

Proof

Draw line a through points A and B. Draw line b through point C and parallel to line a.

Since lines a and b are parallel, <)BAC = <)B'CA and <)ABC = <)BCA'.

It is obvious that <)B'CA + <)ACB + <)BCA' = 180 degrees.

Thus <)ABC + <)BCA + <)CAB = 180 degrees.

Answer 2

Answer:

Draw line a through points A and B. Draw line b through point C and parallel to line a.

triangle

Since lines a and b are parallel, <)BAC = <)B'CA and <)ABC = <)BCA'.

It is obvious that <)B'CA + <)ACB + <)BCA' = 180 degrees.

Thus <)ABC + <)BCA + <)CAB = 180 degrees.