Three Spherical Triangles of Equal Area

point C

1.0472

point B

θ

1.0472

ϕ

1.08331

point A'

0.2

point C'

0.2

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This Demonstration shows three spherical triangles. Triangles

ABC

and

ABC'

have a common base and the same area, so they are equivalent by dissection (as shown in Dissection of Two Spherical Triangles with a Common Base). Triangles

ABC

and

A'BC

also have a common base and the same area, so they are also equivalent by dissection. So triangles

ABC'

and

A'BC

are equivalent by dissection.

Therefore, spherical triangles with the same area are equivalent by dissection.