Properties
Let ABCD be a Saccheri quadrilateral having AB as base, CA and DB the equal sides that are perpendicular to the base and CD the summit. The following properties are valid in any Saccheri quadrilateral in hyperbolic geometry.
- The summit angles (at C and D) are equal and acute.
- The summit is longer than the base.
- The line segment joining the midpoint of the base and the midpoint of the summit is mutually perpendicular to the base and summit.
- The line segment joining the midpoints of the sides is not perpendicular to either side.
- The above two line segments are perpendicular to each other.
- The line segment joining the midpoint of the base and the midpoint of the summit divides the Saccheri quadrilateral into two Lambert quadrilaterals.
- Two Saccheri quadrilaterals with congruent bases and congruent summit angles are congruent (i.e., the remaining pairs of corresponding parts are congruent).
- Two Saccheri quadrilaterals with congruent summits and congruent summit angles are congruent.
Read more about this topic: Saccheri Quadrilateral
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