TrueFalse 16 The ASA criterion for congruence of traingles i

True/False

16) The ASA criterion for congruence of traingles is one of our axioms for neutral geometry

17) A Lambert quadrilateral can be \"doubled\" to form a Saccheri quadrialteral and a Saccheri quadrilateral can be \"halved\" to form a Lambert quadrilateral

18) If triangle ABC is any triangel if a perpendicular is dropped from C to line AB then that perpendicular will intersect line AB in a point between A and B

19) It i a theorem in neutral geometry that given any point P and any line l there is at most one line through P perpendicular to l

20) It is a theorem in neutral geometry that vertical angles are congruent to each other

21) In the sphere interpretation, where \"lines\"are interpreted to be great circles, Euclid V holds, yet the Euclidean parallel postulate does not exist

22) The gap in Euclid\'s attempt to prove Theorem 4.2 can be filled using our axioms of betweeness

Solution

True/False

16) The ASA criterion for congruence of traingles is one of our axioms for neutral geometry False

17) A Lambert quadrilateral can be \"doubled\" to form a Saccheri quadrialteral and a Saccheri quadrilateral can be \"halved\" to form a Lambert quadrilateral

18) If triangle ABC is any triangel if a perpendicular is dropped from C to line AB then that perpendicular will intersect line AB in a point between A and B False

19) It is a theorem in neutral geometry that given any point P and any line l there is at most one line through P perpendicular to l True

20) It is a theorem in neutral geometry that vertical angles are congruent to each other TRUE

21) In the sphere interpretation, where \"lines\"are interpreted to be great circles, Euclid V holds, yet the Euclidean parallel postulate does not exist TRUE

22) The gap in Euclid\'s attempt to prove Theorem 4.2 can be filled using our axioms of betweeness TRUE