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Geometry Solution Manual | Reference Guide Unit 2 | Conditional Statements
Conditional Statements
Solutions
1. Hypothesis: you are riding on a train; conclusion:
8. A.If people shop in Delaware, then they do not
2. Hypothesis: the side length of a square is b;
B.
conclusion: the area of the square is b .
C.
3. Hypothesis: the sum of the measures of two
D.
E.
F. it will stop at every station on the line.
2
angles is 180°; conclusion: the angles are
supplementary angles.
4. Hypothesis: a football player scores a touchdown;
conclusion: the player’s team earns 6 points.
5. A.If a triangle has three congruent sides, then
B.
C.
D.
E.
F.
it has three congruent angles.
A triangle has three congruent sides.
A triangle has three congruent angles.
If a triangle has three congruent angles, then
it has three congruent sides.
If a triangle does not have three congruent
sides, then it does not have three
congruent angles.
If a triangle does not have three congruent
angles, then it does not have three
congruent sides.
6. A. If n = 8, then n2 = 64.
B. n = 8
C. n2 = 64
D. If n2 = 64, then n = 8.
E. If n ≠ 8, then n ≠ 64.
F. If n2 ≠ 64, then n ≠ 8.
9. A. If it is a parallelogram, then it is a rectangle.
B.
C.
D.
E.
F. rectangle.
B. True
12. A. If it is a rectangle, then it is a square.
B. False; not all rectangles are squares.
13. A.If it is a triangle with an obtuse angle, then
it is an obtuse triangle.
B. True
14. A.If it is an isosceles triangle, then it is an
equilateral triangle.
B. False; not all isosceles triangles are
equilateral triangles.
15. A.If coplanar lines are parallel, then they do
not intersect.
B. True
16. A.If a woman is an athlete, then she plays in
soccer’s World Cup.
B. False; not all athletes play in soccer’s
World Cup.
17. A.If lines intersect at right angles, then they
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three acute angles.
B. True
11. A.If it has four right angles, then it is a
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one angle greater than 90°.
A triangle is an obtuse triangle.
A triangle has one angle greater than 90°.
If a triangle has one angle greater than 90°,
then it is an obtuse triangle.
If a triangle is not an obtuse triangle, then it
does not have one angle greater than 90°.
If a triangle does not have one angle greater
than 90°, then it is not an obtuse triangle.
B. False; not all parallelograms are rectangles.
10. A.If a triangle is an acute triangle, then it has
7. A.If a triangle is an obtuse triangle, then it has
pay a sales tax.
People shop in Delaware.
People do not pay a sales tax.
If people do not pay a sales tax, then they
shop in Delaware.
If people do not shop in Delaware, then they
pay a sales tax.
If people pay a sales tax, then they do not
shop in Delaware.
are perpendicular.
B. True
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Geometry Solution Manual | Reference Guide Unit 2 | Conditional Statements
18. A.If a figure does not have four right angles,
26. A.If n is an even number, then n + 1 is an
B.
C.
D.
E.
then it is not a rectangle.
B. True
19. A.If a figure does not have three sides of three
different lengths, then it is not a scalene
triangle.
B. True
20. A.If a figure does not have five congruent sides,
then it is not an equilateral pentagon.
B. True
21. A.If a figure is not a rectangle, then it is not
a square.
B. True
27. A.If a triangle is an isosceles triangle, then it
B.
22. A.If a triangle is not an isosceles triangle, then
C.
D.
E.
it is not an equilateral triangle.
B. True
23. A.If a figure is not a rhombus, then it is not
a square.
B. True
24. A. If angles are vertical, then they are congruent.
B. If angles are congruent, then they are vertical.
C. If angles are not vertical, then they are not
congruent.
D. If angles are not congruent, then they are not
vertical.
E. The conditional and contrapositive are true.
The converse and inverse are false. Angles
that are not vertical can be congruent, such as
right angles.
25. A.If angles are complementary, then they
B.
C.
D.
E.
are acute.
If angles are acute, then they are
complementary.
If angles are not complementary, then they
are not acute.
If angles are not acute, then they are not
complementary.
The conditional and contrapositive are true.
The inverse and converse are false. Angles
that measure 30° and 45° are acute but not
complementary.
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odd number.
If n + 1 is an odd number, then n is an
even number.
If n is not an even number, then n + 1 is not
an odd number.
If n + 1 is not an odd number, then n is not
an even number.
The conditional, converse, inverse, and
contrapositive are true.
has at least two congruent sides.
If a triangle has at least two congruent sides,
then it is an isosceles triangle.
If a triangle is not an isosceles triangle, then
it does not have at least two congruent sides.
If a triangle does not have at least two
congruent sides, then it is not an isosceles
triangle.
The conditional, converse, inverse, and
contrapositive are true.
28. A.If n is a whole number, then an even number
B.
C.
D.
E.
can be written in the form 2n.
If an even number can be written in the form
2n, then n is a whole number.
If n is not a whole number, than an even
number cannot be written in the form 2n.
If an even number cannot be written in the
form 2n, then n is not a whole number.
The conditional, converse, inverse, and
contrapositive are true.
29.
Statement
p
q
T
T
F
F
T
F
T
F
p
q
T
F
T
T
Converse
q
p
T
T
F
T
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Geometry Solution Manual | Reference Guide Unit 2 | Conditional Statements
30.
Statement
p
q
T
T
F
F
T
F
T
F
31.
p
q
T
T
F
F
T
F
T
F
p
q
Contrapositive
~q
~p
T
F
T
T
T
F
T
T
Statement
Inverse
q
p
~p
T
F
T
T
38. A.If a figure is square, then it is a rectangle.
39. A.If a person is a drummer, then he is a
~q
T
T
F
T
32. If a statement is true, then its contrapositive is
points lie
in the
third quadrant
both coordinates
of points are
negative
33. If a statement is false, then its contrapositive is false.
41.
travels
from
United States
to
England
34. A.If a whole number has a factor of 2, then the
percussionist.
If a person is a percussionist, then he is in an
orchestra.
Therefore, if a person is a drummer, then he
is in an orchestra.
B. False
40.
true. However, the inverse is true only when the
converse is true. For example, the statement “If
it is a right angle, it is 90°” has a true converse
and inverse. But the statement “If two lines are
perpendicular, then they intersect” has a false
converse and inverse.
However, the inverse is true only when the converse
is true. For example, the statement “If it lives in the
ocean, it is a fish” has a true converse and inverse.
The statement “If a polygon has five sides, it is a
square” has a false converse and inverse.
If a figure is a rectangle, then it is a
parallelogram.
If a figure is a parallelogram, then it is a
quadrilateral.
Therefore, if a figure is a square, then it is a
quadrilateral.
B. True
whole number is an even number.
B. True
has a passport
35. A.If two lines are perpendicular, then the lines
intersect to form right angles.
B. True
36. A.If a person is an Olympian, the person is an
athlete.
B. True
37. A.If a triangle is an equilateral triangle, then
the triangle is an isosceles triangle.
B. True
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42.
angles
form a
linear
pair
supplementary
angles
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Geometry Solution Manual | Reference Guide Unit 2 | Conditional Statements
43.
46.
points
X, Y, and
Z are on
line m
parallel
lines
three points
on same line
coplanar
lines that do
not intersect
collinear points
44.
47.
segment
bisector
Phoenix
line, ray, or segment
that divides segment
into two congruent
parts
Arizona
Southwest
45.
United States
glass
object
fragile
object
handle with care
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Copying or distributing without K12’s written consent is prohibited.
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