Geometry Practice Test 1

Problem (1) Which of the following are contingencies:
(a) (b) (c) (d) (e)

Problem (2) Which of the following are contradictions:
(a) (b) (c) (d) (e)

Problem (3) Which of the following are tautologies:
(a) (b) (c) (d) (e)

Problem (4) Expressions that are synonymous with "P lies on " are
(a) (b) is incident with (c) is incident with (d) (e) none of the above

Problem (5) The axioms on the handout are due to
(a) Euclid (b) Legrendre (c) Hilbert (d) Pythagoreans (e) none of the above

Problem (6) Which of the following needs a proof:
(a) Theorem (b) Proposition (c) Axiom (d) Definition (e) Postulate (e) none of the above

Problem (7) Which is the negation of the statement: "if 3 is an odd number then 9 is odd"
(a) "3 is an odd number and 9 is even" (b) "3 is an even number and 9 is even" (c) "3 is an even number and 9 is odd" (d) "3 is an odd number or 9 is even" (e) none of the above

Problem (8) The negation of the statement: "If a line intersects one of two parallel lines, it also intersects the other." is
(a) A line intersects one of two parallel lines and does not intersect the other.
(b) There exists two parallel lines and a line that intersects one of them and does not intersect the other.
(c) If a line intersects one of two parallel lines, it does not intersect the other.
(d) There exists two parallel lines and a line that intersects one of them must intersect both of them.
(e) none of the above

Problem (9) Euclid stated that all right angles are congruent to each other and justified this by:
(a) axiom (b) definition (c) postulate (d) a proof (e) none of the above

Problem (10) Euclid stated that lines are parallel if they do not intersect and justified this by:
(a) axiom (b) definition (c) postulate (d) a proof (e) none of the above

Problem (11) Negate Incident Axiom (i).
(a) There exists two distinct points with no line passing through them or if there is a line passing through them it is not unique.
(b) There exists two distinct points and every line passing through them it is not unique.
(c) For every two points there is no unique line passing through them.
(d) For every two points there is no line passing through them or if there is a line passing through them it is not unique.
(e) none of the above.

Problem (12) Negate Incident Axiom (ii).
(a) There exists a line with no points on it or only one point on it.
(b) There exists a line with only one point on it.
(a) Every line has no points on it or only one point on it.
(b) Every line has only one point on it.
(e) none of the above

Problem (13) Rewrite Incident Axiom (iii) as a conjunction.
(a) There exists three distinct point and
(b) There exists distinct point and and at least one of these points does not lie on a line.
(c) There exists distinct point and and for every line, at least one of these points does not lie on the line.
(d) There exists distinct point and and there exists a line with at least one of these points not on it.
(e) none of the above

Problem (14) Suppose someone is proving a proposition by using the contrapositive and the RAA Method. An assumption in the proof would be:
(a) (b) (c) (d) (e) none of the above.

Problem (15) Prove that for every point there is at least one line not passing through it.

Problem (16) Prove that for every line there is at least one point not lying on it.

Problem (17) Prove the following statement is true: If is any line, then there exist lines and such that and are distinct and both and intersect

Cite this as:
Geometry Practice Test 1
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/geometry-practice-test-1.html