In a spherical triangle ABC do the following properties hold?
(a) If AB = AC are the base angles at B and C equal? Yes
(b) If the angles at B and C are equal is it true that AB = AC? Yes
(c) Do the angles add to 180◦? No
(d) Do the sides add to 180◦? No
(e) If C = 90◦ is it true that AB$^2$ = BC$^2$ + CA$^2$? No, it is cos(C/R) = cos(A/R) cos(B/R)
(f) Do two triangles with equal corresponding sides have equal corresponding angles? Yes
(g) Do two triangles with equal corresponding angles have equal corresponding sides? Yes.
If anyone can verify that would be helpful.
Best Answer
Everything is right
(a) can be proven true by law of sines
(b) can be proven true by law of sines
(c) false through the idea of area in a spherical triangle
(d) False, you can have a small triangle less than 180 or bigger.
(e) it is false but you do not have the right reason, try plugging in the value since AB ,BC and CA are the lengths.
(f) True through law of cosine
(g) True through polar law of cosines