Question

Prove that sum of angles of a triangle is equal to 180°

Answer 1

hlo mate.

here is your answer.

__________________

We know that there are 3 angles in a triangle .
and each of the angles measures 60 degree.
=>60 × 3
=>180 degree.

__________________


hope it helps you

Answer 2

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.

Lemma
If ABCD is a quadrilateral and <)CAB = <)DCA then AB and DC are parallel.

Proof
Assume to the contrary that AB and DC are not parallel.
Draw a line trough A and B and draw a line trough D and C.
These lines are not parallel so they cross at one point. Call this point E.


Notice that <)AEC is greater than 0.
Since <)CAB = <)DCA, <)CAE + <)ACE = 180 degrees.
Hence <)AEC + <)CAE + <)ACE is greater than 180 degrees.
Contradiction. This completes the proof.

Definition
Two Triangles ABC and A'B'C' are congruent if and only if
|AB| = |A'B'|, |AC| = |A'C'|, |BC| = |B'C'| and,
<)ABC = <)A'B'C', <)BCA = <)B'C'A', <)CAB = <)C'A'B'.