Question

Describe the Saccheri Quadrilateral and prove in neutral geometry that the summit angles are congruent.

Answer #1

show that if the summit and the base angles of two saccheri
quadrilaterals are congruent then the reamining sides are
congruent.

prove
in a saccheri quadrilateral, the length of the summit is greater
than the length of the base

Prove in hyperbolic geometry: If two Saccheri quadrilaterals
have congruent bases and congruent summits, then they are
congruent.

Prove that equilateral triangles exist in
neutral geometry (that is, describe a construction
that will yield an equilateral triangle). note that all the
interior angles of an equilateral triangle will be congruent, but
you don’t know that the measures of those interior angles is
60◦.Also, not allowed to use circles.

Corollary 6.1.10. In a Saccheri quadrilateral, the length of the
summit is greater than the length of the base.
please proof

Neutral Geometry Proof:
If two lines are cut by a transversal and
the alternate interior angles are congruent, or
the corresponding angle are congruent, or
the interior angles on the same side are supplementary, then the
lines are parallel.

Prove: If two angles of a triangle are not congruent, then the
sides opposite those angles are not congruent.

Neutral Geometry Proof
If two parallel lines are cut by a transversal, then
The alternate interior angles are congruent.
The corresponding angles are congruent.
The interior angles on the same side are supplementary.

formally/step by step: prove that similar but non-congruent
triangles cannot exist in elliptic geometry

Prove (with neutral geometry)
If the angle of parallelism for a point P and a line RS is
Less Than 90 degrees, then there exist At Least Two lines through P
that are parallel to line RS.
Please explain step by step and include a diagram. Thanks so
much!

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