Saccheri quadrilaterals; Lambert quadrilaterals
Draw a diagram of a Saccheri quadrilateral ABDC, where
(a) A and B are a pair of consecutive vertices
(b) sides AD and BC are a pair of opposite sides
(c) angles A and B are right angles
(d) sides AD and BC are congruent.
Then let M be the midpoint of AB, and drop a perpendicular from M to CD with foot N.
Once that is done, show that AMND and BMNC are Lambert quadrilaterals.
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In an attached .doc file (310.33-Solution.doc), the diagram is drawn, the definitions of Saccheri quadrilateral and Lambert quadrilateral are reviewed, and a detailed ...
Solution Summary
The diagram is drawn, and a detailed, two-column proof of the given assertion (that if certain specified geometric constructions are performed on the given Saccheri quadrilateral, then two specific quadrilaterals in the resulting diagram are Lambert quadrilaterals) is presented. The definitions of Saccheri quadrilateral and Lambert quadrilateral are reviewed.