What Is a Corollary in Geometry?

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In geometry, a corollary is a statement that is proven true by another statement or considered to be a consequence of a statement's truth. Corollaries are believed to be true without additional proof besides the initial true statement.

An example of a corollary is that an equilateral triangle is always equiangular because it is known that on a triangle, angles that oppose two congruent sides are always congruent. Because the triangle has all congruent or equal sides, it is equilateral. Because the angles are congruent, the triangle is equiangular, or with equal angles. Therefore, the corollary is known as true by the original statement or theorem.