Answer to Question #139276 in Trigonometry for riz

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 "A" and "B", and the third angle be at vertex "C". Now, we draw a line segment from "C" to the midpoint of "\\overline{AB}" which we call "M".


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




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

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




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