In △ABC, ∠A, ∠B and ∠C are three internal angles. To prove ∠A+∠B+∠C= 180, that is, to prove ∠A+∠b+∞.

-This needs to be proved by the nature of parallel lines: two straight lines are parallel, the same angle is equal, the inner angle is equal, and the inner angles on the same side are complementary.

It is proved that the sum of internal angles of triangle is 180.

Proof method 1:

(1) Extend BC to D (using the true proposition that "line segments can be extended")

(2) Make CE∨AB at point C (use "a parallel line, which can be a known straight line passing through a point outside the straight line").

(3)∠A=∠ 1 (using "two straight lines are parallel and the internal angles are equal")

(4)∠B=∠2 (using "two straight lines are parallel and the same angle is equal")

(5) ∠ 1+∠ 2+∠ ACB = 180 (using "the degree of a flat angle")

(6)∠A+∠B+∠ACB=∠ 1+∠2+∠C (use "equivalent substitution")

(7) ∠ A+∠ B+∠ ACB = 180 (using "equivalent substitution")

It is proved that the sum of internal angles of triangle is 180.

Proof method 2:

(1) The crossing point A is PQ∨BC.

(2)∠ 1=∠B (two straight lines are parallel and the internal dislocation angles are equal)

(3)∠2=∠C (two straight lines are parallel and the internal dislocation angles are equal)

(4)≈ 1+∠2+∠3 = 180 (definition of right angle)

(5) ∴∠ BAC+∠ B+∠ C = 180 (equivalent substitution)

The triangle and the inner angle of 180.

Proof method 3:

(1) If point A is PQ∨BC, then

(2)∠ 1=∠C (two straight lines are parallel and the internal dislocation angles are equal)

(3)≈baq+∠b = 180 (two straight lines are parallel and their internal angles are complementary)

(4) and ? baq = ∠1+∠ 2 (definition of right angle)

(5) ∴∠ 2+∠ B+∠ C = 180 (equivalent substitution)

It is proved that the sum of internal angles of triangle is 180.

Proof method 4:

Take a little D from BC, make it into DE∨BA and DF∨CA, and hand it over to AC to E and AB to F respectively.

(1) has ∠ 2 = ∠2=∠B, ∠ 3 = ∠3=∠C (two straight lines are parallel and have equal angles).

(2) ∠ 1 = ∠ 4 (two straight lines are parallel and the internal dislocation angles are equal)

(3) ∠ 4 = ∠ A (two straight lines are parallel and have the same included angle)

(4) ∴∠ 1 = ∠ A (equivalent substitution)

(5)≈ 1+∠2+∠3 = 180 (definition of right angle)

(6)∴∠A+∠B+∠C= 180。

The triangle and the inner angle of 180.