Geometry Practice Test 11

(1) In hyperbolic geometry,
    (a) a rectangle exists                    
    (b) all triangles have angle sum of     
    (c)  some triangles have angle sum of          
    (d) there are no rectangles

(2) In Euclidean geometry,   (recall "defective triangle" means the defect of the triangle is zero)
    (a) if one defective triangle exists then all triangles are defective,
    (b) there are some defective triangles
    (c) the sum of any two angles in a triangle is less than or equal to
    (d)  none of the above

(3) In neutral geometry,
    (a) if a defective triangle does not exist, then a rectangle exists.
    (b)  if a defective triangle does exist, then a rectangle exists.
    (c) none of the above

(4) Given the hypothesis of Wallis' postulate, namely:  Given any triangle and given any segment ; the conclusion of Wallis' postulate is:
    (a) there exists a triangle (having as one of its angles) that is congruent to     
    (b) there exists a triangle (having as one of its angles) that is similiar to     
    (c) there exists a triangle (having as one of its sides) that is similiar to  
    (d) none of the above

(5) Clairaut's Axiom states:
    (a) there are no rectangles
    (b) Euclid's fifth postulate is equivalent to Hilbert's parallel postulate
    (c) Hilbert's parallel postulate  is equivalent to the angle sum of every triangle is
    (d) none of the above

(6) The Universal Hyperbolic Theorem states that,
    (a) for every line and every point not on line there pass through at least two distinct parallels to
    (a) for every line and every point not on line there pass through exactly two distinct parallels to
    (a) for every line and every point not on line there pass through at least one distinct parallels to
    (a) for every line and every point not on line there pass through exactly one distinct parallels to

(7) The triangle congruence criterion is valid in
    (a) neutral geometry only
    (b) Euclidean geometry only
    (c) Euclidean geometry and hyperbolic geometry
    (d) hyperbolic geometry only     

(8) Define Hyperbolic geometry.
    

(9) Given a ray between and prove that there exists a segment whose two endpoints are on the opposite rays of   and respectively and such that the opposite ray of intersects this segment.
    

(10) Given segment prove that there exists points such that , and
    

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Geometry Practice Test 11
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/geometry-practice-test-11.html