Question #139276
Prove that, If 2 angles of a spherical triangle are equal, then the triangle is an isosceles spherical triangle.
1
Expert's answer
2020-10-20T18:23:57-0400

Let the two equal angles be at vertex AA and BB, and the third angle be at vertex CC. Now, we draw a line segment from CC to the midpoint of AB\overline{AB} which we call MM.


Then we have two triangles AMC\triangle{AMC} and BMC\triangle{BMC}, which are congruent by the SAS rule.




Since AC\overline{AC} and BC\overline{BC} are equal

\therefore two sides of the spherical triangle ABC\triangle {ABC} are equal making it an isosceles spherical triangle




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