Corollary: 11.35: Condition for Equal Angles contained by Elevated Straight Lines from Plane Angles
(related to Proposition: Prop. 11.35: Condition for Equal Angles contained by Elevated Straight Lines from Plane Angles)
(Corollary to Proposition 35 from Book 11 of Euclid's “Elements”)
So, it is clear, from this, that if there are two equal rectilinear angles, and equal raised straight lines are stood on them (at their apexes), containing equal angles respectively with the original straight lines (forming the angles), then the perpendiculars drawn from (the raised ends of) them to the planes in which the original angles lie are equal to one another. (Which is) the very thing it was required to show.
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Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"