Proof
Construct the parallelogram joining corresponding points; by I.33
opposite sides are equal, and by I.8 (SSS) the two triangles formed
at the vertex angles are congruent.
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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.33Proposition I.33The straight lines joining equal and parallel straight lines (at the extremities which are in the same directions) are…
- 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…
Required by (dependents) (4)
- XI.15Proposition XI.15If two straight lines meeting one another be parallel to two straight lines meeting one another, not being in the same…
- XI.24Proposition XI.24If a solid be contained by parallel planes, the opposite planes in it are equal and similar parallelograms.
- XI.26Proposition XI.26At a given point on a given straight line to construct a solid angle equal to a given solid angle contained by three…
- XI.35Proposition XI.35If there be two equal plane angles, and on their vertices there be set up elevated straight lines containing equal…
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