Proof
Apply I.4 to the resulting two triangles and I.29 + I.27 for
parallelism.
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Full neighborhood
Depends on (3)
- I.4Proposition I.4If two triangles have two sides equal to two sides respectively, and have the angles contained by the equal straight…
- I.27Proposition I.27If a straight line falling on two straight lines make the alternate angles equal to one another, the straight lines…
- I.29Proposition I.29A straight line falling on parallel straight lines makes the alternate angles equal to one another, the exterior angle…
Required by (dependents) (4)
- I.36Proposition I.36Parallelograms which are on equal bases and in the same parallels are equal to one another.
- XI.9Proposition XI.9Straight lines which are parallel to the same straight line and are not in the same plane with it are also parallel to…
- XI.10Proposition XI.10If two straight lines meeting one another be parallel to two straight lines meeting one another, not in the same plane,…
- XI.24Proposition XI.24If a solid be contained by parallel planes, the opposite planes in it are equal and similar parallelograms.
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