Proof
Same scheme as VI.5: extend one triangle so as to match the second
on the equal-angle pair (I.23), apply VI.4 to deduce the missing
side, then I.4 (SAS) for congruence of the auxiliary triangle with
the second.
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Depends on (4)
- I.4Proposition I.4If two triangles have two sides equal to two sides respectively, and have the angles contained by the equal straight…
- 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…
- VI.5Proposition VI.5If two triangles have their sides proportional, the triangles will be equiangular and will have those angles equal…
Required by (dependents) (2)
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