Geometry Practice Test 9

(1) An angle is defined as the space between two rays that emanate from the same point.    
    (a) True    
    (b)  False

(2) Which of the following is equivalent to the contrapositive of  
    (a)       
    (b)          
    (c)       
    (d)         
    (e)  none of these     

(3) Euclid proved that every right angle is ______________.
        (a) congruent to a right angle.      
        (b) congruent to itself.           
        (c) none of the above      

(4) There exists four non-collinear points.
    (a) True        
    (b)  False        
    (c)  Not provable     

(6)  Euclid neglected to state which of the following assumptions:
    (a) points and line exists
    (b) all points are collinear
    (c) not every line has two points on it
    (d) none of the above

(7)  Eulid never used the notion of "betweeness" and instead
    (a) ignored it
    (b) used diagrams
    (c) forgot it

(8) Hilbert's system of axioms for geometry  _______.  
    (a) came before Euclid's system.
    (b) was the first since Euclid's system.
    (c) came much later after Non-Euclidean geometry was discovered.
    (d) none of the above

(9)  Hilbert was quoted as saying, "We must be able to say at all times -- instead of ________ --- tables, chairs, and beer.
    (a) betweenness, congruence, and continuity
    (b) axioms, postulates, and definitions
    (c) points, lines, and planes
    (d) none of the above

(10)  Given distinct points and The order axioms says,
    (a)
    (b) or  
    (c) precislely one of ,   or
    (d) precislely one of ,   or
    (e) none of the above

(11)  Which ensures that lines are not circular:
    (a) Plane seperation axiom
    (b) Order axiom
    (c) Pasch theorem
    (d) Crossbar theorem
    (e) none of the above

(12)  We did not assume the line seperation property as an axiom but instead, we
    (a) proved it as a consequence of our plane sepration axiom (and others)
    (b) proved it as a consequence of our Pasch Theorem (and others)
    (c) proved it as a consequence of our Crossbar Theorem (and others)
    (d) proved it as a consequence of our three Point Property (and others)

(13)  Which indirectly guarantees that our geometry is two-dimensional:
    (a) Plane seperation axiom
    (b) Order axiom
    (c) Pasch theorem
    (d) Crossbar theorem
    (e) none of the above

(14)  Which was Euclid using without proof:
    (a) Plane seperation axiom
    (b) Order axiom
    (c) Pasch theorem
    (d) Crossbar theorem
    (e) none of the above

(15) Given If is a point not on the line determined by and then and are on opposite sides of

(16)  If and are distinct noncollinear points and is any line intersecting in a point between and then also intersects  either or If does not lie on then does not intersect both and

(17) Prove the following statement is true: If is any point, then there exist points and such that , and are noncollinear.

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