True/False 16) The ASA criterion for congruence of traingles is one of our axiom
ID: 3405589 • Letter: T
Question
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
Explanation / Answer
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
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