Can a Saccheri Quadrilateral have 3 congruent sides? I know the summit is less then the base, but could it happen that the base is the same length as the two vertical sides?
Asked
Active
Viewed 224 times
1
-
To make sure we agree on definitions: A Saccheri quadrilateral is one with two equal sides lying at right angles to the base. There's no stipulation about the relative length of the base, so the answer to your question(s) is "Yes". (BTW, the summit edge is longer than the base edge in hyperbolic geometry. (Well, they're congruent if they both have zero length.)) – Blue Apr 28 '13 at 05:59
1 Answers
1
Yes, a Saccheri Quadrilateral with three congruent and one larger side is possible. The following image is a screenshot of the hyperbolic plane, rendered in the Poincaré disc model, with a construction executed using Cinderella.
MvG
- 42,596