Proposition VI.5 — If two triangles have their sides proportional, the triangle…

Proof

Construct on the second triangle's base a triangle equiangular with the first (I.23); by VI.4 its other sides are determined by the proportion, and by I.8 (SSS) it coincides with the second triangle. Therefore the second triangle is equiangular with the first.

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Depends on (3)

I.8Proposition I.8If two triangles have the two sides equal to two sides respectively, and have also the base equal to the base, they…
I.23Proposition I.23On a given straight line and at a point on it to construct a rectilineal angle equal to a given rectilineal angle.
VI.4Proposition VI.4In equiangular triangles the sides about the equal angles are proportional, and those are corresponding sides which…

Required by (dependents) (1)

VI.6Proposition VI.6If two triangles have one angle equal to one angle and the sides about the equal angles proportional, the triangles…

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