Prove: If the sum of the angles of a triangle is a constant n, then...

mravinjakag

mravinjakag

Answered

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

Expert

2022-06-28Added 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.

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