Question

Identify the statement that is true in spherical geometry.
a.
The shortest distance between two points is the length of an arc of a great circle.
b.
Two distinct lines intersect in exactly three points.
c.
Through two given points, there is one and only one line.
d.
If a triangle contains a right angle, then its other two angles are complementary.

Answer 1

http://www.mathsisfun.com/geometry/complementary-angles.html

Answer 2

i think its D

Answer 3

@ME_LLAMO_NICK The link you posted refers to a theorem in EUCLIDEAN Geometry. SPHERICAL Geometry is a type of non-Euclidean Geometry. The theorems are not necessarily the same.

Answer 4

@kelsi1997

I was reading about spherical geometry here:

http://math.youngzones.org/Non-Egeometry/spherical.html

Answer 5

I think that this option is NOT correct: d.
If a triangle contains a right angle, then its other two angles are complementary.

That is because the sum of the angles of a spherical triangle is greater than 180.

Answer 6

By the way, do more reading here:
http://tinyurl.com/maqsph8

Answer 7

I think this option is not correct:
c.
Through two given points, there is one and only one line.

That is because in spherical Geometry, infinitely many "lines" (great circles) may pass through the same two points. Example: given the two antipodal points of "North and South Pole."

Answer 8

Of options A and B, which do you think may be the correct statement. You can do more reading here:

http://h2g2.com/approved_entry/A974397