Prove: If the sum of the angles of a triangle

mravinjakag

mravinjakag

Answered question

2022-06-27

Prove: If the sum of the angles of a triangle is a constant n, then n = 180 and thus the geometry is Euclidean

Answer & Explanation

Angelo Murray

Angelo Murray

Beginner2022-06-28Added 23 answers

Step 1
Here:
1) A + B + C = n (constant)
Step 2
Two parallel lines l 1 and l 2 , such that l 1 passes through A and l 2 passes through side BC.
From the property of straight line:
1 + A + 2 = 180 ( 2 )
Also,
From the property of alternate interior angles:
{ 1 = B 2 = C ( 3 )
Step 3
Using (2) and (3):
A + B + C = 180 °
Hence, from (1):
n = 180
The above figure is a 2-dimensional plane figure with sum of all angles 180.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Elementary geometry

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?