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Corollary: Angles and Sides in a Triangle V

(related to Proposition: 1.25: Angles and Sides in a Triangle IV)

In two triangles with two pairs of sides respectively equal to the other, the final sides are unequal if and only if the interior angles of the two pairs of sides are also unequal. Specifically, the statement that

"the triangle with the longer side contains a greater interior angle than the triangle with the shorter side"

is equivalent to the statement that

"the triangle with the greater interior angle has a longer base than the triangle with the lesser interior angle".

Table of Contents

Proofs: 1

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References

Adapted from CC BY-SA 3.0 Sources:

1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014

Adapted from (Public Domain)

1. Casey, John: "The First Six Books of the Elements of Euclid"