Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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Write the inverse of the conditional statement. Determine whether the inverse
is true or false. If it is false, find a counterexample.
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1.
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If you have a gerbil, then you are a pet owner.
a. | If you are not a pet owner, then you do not have a gerbil. True | b. | If you do not have a
gerbil, then you are not a pet owner. False; you could have a dog. | c. | If you are not a pet
owner, then you have a gerbil. False; if you are not a pet owner then you have no
pets. | d. | If you are not a gerbil, then you are not a pet owner.
True |
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2.
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All country names are capitalized words.
a. | All capitalized words are country names. False; the first word in the sentence is
capitalized. | b. | All non-capitalized words are not country names. True | c. | No country name is
capitalized. False; Canada is capitalized. | d. | No country name is not capitalized. True; all
country names are proper nouns, and thus capitalized. |
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3.
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Independence Day in the United States is July 4.
a. | July 4 is not Independence Day in the United States. False; it is Independence
Day. | b. | Days that are not Independence Day are not July 4. True | c. | Days that are not
Independence Day are July 4. False; July 4 is Independence Day in the United
States. | d. | Days that are not July 4 are not Independence Day in the United States.
True |
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4.
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Thanksgiving Day in the United States is November 25.
a. | If it is not November 25, it is Thanksgiving Day in the United States.
True | b. | If it is not Thanksgiving Day in the United States, it is not November 25. False;
Thanksgiving Day could be another date in a different year so November 25 could be not Thanksgiving
Day. | c. | If it is not November 25, it is not Thanksgiving Day in the United States.
True | d. | If it is not November 25, it is not Thanksgiving Day in the United States. False;
Thanksgiving Day could be another date in a different year. |
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5.
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Two angles measuring 180 are supplementary.
a. | Two angles not measuring 180 are supplementary. False | b. | More than two angles
measuring 180 are non-supplementary. True | c. | Two angles not measuring 180 are not
supplementary. True | d. | Non-supplementary angles are two angles not
measuring 180. True |
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Determine whether the conjecture is true or false. Give a
counterexample for any false conjecture.
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6.
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Given:  are coplanar. Conjecture: They are vertical
angles.
a. | False; the angles may be supplementary. | b. | True | c. | False; one angle may be in the interior of the
other. | d. | False; the angles may be adjacent. |
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7.
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Given:  is supplementary to  and  is supplementary
to  . Conjecture:  is supplementary to  .
a. | False; they could be right angles. | b. | False; they could be congruent
angles. | c. | True | d. | False; they could be vertical
angles. |
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8.
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Given:
Conjecture: 
a. | False; the angles are not vertical. | b. | True | c. | False; the angles
are not complementary. | d. | False; there is no indication of the measures
of the angles. |
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9.
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Given: a concave polygon
Conjecture: It can be regular or
irregular.
a. | False; to be concave the angles cannot be congruent. | b. | True | c. | False; all concave polygons are
regular. | d. | False; a concave polygon has an odd number of sides. |
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10.
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Given: segments RT and ST; twice the measure of  .
Conjecture: S is the
midpoint of segment RT.
a. | True | b. | False; point S may not be on  . | c. | False; lines do not have midpoints. | d. | False;  could be the segment
bisector of  . |
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Choose the corresponding statement in spherical geometry for each property of
plane Euclidean geometry.
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11.
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A plane is a flat surface made up of points that extend infinitely in all
directions.
a. | A plane is a flat surface made up of points that extend infinitely in all
directions. | b. | A plane is a flat surface that divides the sphere into two
hemispheres. | c. | A plane is the surface of the sphere. | d. | There is no corresponding
statement. |
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12.
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Perpendicular lines intersect at one point.
a. | Perpendicular lines intersect at one point. | b. | Perpendicular great
circles intersect at one point. | c. | Perpendicular great circles intersect at two
points. | d. | There is no corresponding statement. |
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13.
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The shortest path between two points is a line segment.
a. | The shortest path between two points on a sphere is a line
segment. | b. | The shortest path between two points on a sphere is an arc. | c. | The shortest path
between two points on a sphere is a triangle. | d. | There is no corresponding statement.
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14.
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If two lines are perpendicular to a third line, they are parallel.
a. | If two lines are perpendicular to a third line, they are
parallel. | b. | If two great circles are perpendicular to a third line, they are
parallel. | c. | If two great circles are parallel to a third line, they are
parallel. | d. | There is no corresponding statement. |
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15.
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Perpendicular lines form 90° angles.
a. | Perpendicular great circles form 90° angles. | b. | Perpendicular great
circles form angles less than 90°. | c. | Perpendicular great circles form angles more
than 90°. | d. | There is no corresponding statement. |
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16.
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A triangle can have at most one obtuse angle.
a. | A triangle can have at most one obtuse angle. | b. | A triangle can have
at most two obtuse angles. | c. | A triangle can have at most three obtuse
angles. | d. | There is no corresponding statement. |
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17.
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Given a line and a point not on the line, there exists exactly one line through
the point that is parallel to the given line.
a. | Given a great circle and a point not on the great circle, there exists exactly one
great circle through the point that is parallel to the given great circle. | b. | Given a great circle
and a point not on the great circle, there exists exactly two great circles through the point that is
parallel to the given great circle. | c. | Given a great circle and a point not on the
great circle, there exists infinitely many great circles through the point that is parallel to the
given great circle. | d. | There is no corresponding
statement. |
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18.
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The sum of the angles of a triangle is 180°.
a. | The sum of the angles of a triangle is 180°. | b. | The sum of the
angles of a triangle is less than 180°. | c. | The sum of the angles of a triangle is more
than 180°. | d. | There is no corresponding statement. |
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19.
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Three noncollinear points determine a triangle.
a. | Three noncollinear points determine a triangle. | b. | Three collinear
points determine a triangle. | c. | Two noncollinear points determine a
triangle. | d. | There is no corresponding statement. |
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20.
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All equilateral triangles are similar.
a. | All equilateral triangles are similar. | b. | All equilateral triangles are
congruent. | c. | No equilateral triangles are similar. | d. | There is no corresponding
statement. |
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