The two triangles have equal radii as corresponding sides and equal chord lengths as their bases. Therefore, all three corresponding sides are equal, so the triangles are congruent by the SSS Congruence Criterion.
Show that if two such isosceles triangles (occurring in the previous question) have equal base length, they are congruent to each other.
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Consider two triangles formed by equal chords and the centre of the same circle. Each triangle has two sides equal to the radii of the circle, and the given base lengths are also equal. Thus, all three corresponding sides of the triangles are equal. Therefore, the triangles are congruent by the SSS Congruence Criterion.
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