Question

prove exprimently that the sum of three angles of a triangle is equal to two right .​

Answer 1

Answer:

Proof 1

Euclid-I-32.png

Let △ABC be a triangle.

Let BC be extended to a point D.

From External Angle of Triangle equals Sum of other Internal Angles:

∠ACD=∠ABC+∠BAC

Bby by Euclid's Second Common Notion:

∠ACB+∠ACD=∠ABC+∠BAC+∠ACB

But from Two Angles on Straight Line make Two Right Angles, ∠ACB+∠ACD equals two right angles.

So by Euclid's First Common Notion, ∠ABC+∠BAC+∠ACB equals two right angles.

■In a triangle, the sum of the three interior angles equals two right angles. In the words of Euclid: In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of the triangle are equal to two right angles.Oct 8, 2019