Proof
By XI.7 the connecting segment lies in the plane of the parallels;
combine XI.4 (perpendicularity transferred along parallel lines via
shared plane structure) with I.29 (alternate angles) to obtain
perpendicularity of the second line.
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Depends on (4)
- I.29Proposition I.29A straight line falling on parallel straight lines makes the alternate angles equal to one another, the exterior angle…
- XI.4Proposition XI.4If a straight line be set up at right angles to two straight lines which cut one another, at their common point of…
- XI.6Proposition XI.6If two straight lines be at right angles to the same plane, the straight lines will be parallel.
- XI.7Proposition XI.7If two straight lines be parallel, and points be taken at random on each of them, the straight line joining the points…
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