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GEO - Chapter 2 Test Review
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Identify the hypothesis and conclusion of this conditional statement:
If two lines intersect at right angles, then the two lines are perpendicular.
a. Hypothesis: The two lines are perpendicular. Conclusion: Two lines intersect at right
angles.
b. Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are
perpendicular.
c. Hypothesis: The two lines are not perpendicular. Conclusion: Two lines intersect at right angles.
d. Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are not
perpendicular.
b. Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are
perpendicular.
Write this statement as a conditional in if-then form: All triangles have three sides.
a. If a triangle has three sides, then all triangles have three sides.
b. If a figure has three sides, then it is not a triangle.
c. If a figure is a triangle, then all triangles have three sides.
d. If a figure is a triangle, then it has three sides.
d. If a figure is a triangle, then it has three sides.
Which statement is a counterexample for the following conditional? If you live in Springfield, then you live in Illinois.
a. Sara Lucas lives in Springfield.
b. Jonah Lincoln lives in Springfield, Illinois.
c. Billy Jones lives in Chicago, Illinois.
d. Erin Naismith lives in Springfield, Massachusetts.
d. Erin Naismith lives in Springfield, Massachusetts.
Another name for an if-then statement is a ____. Every conditional has two parts. The part following if is the ____ and the part following then is the ____.
a. conditional; conclusion; hypothesis
b. hypothesis; conclusion; conditional
c. conditional; hypothesis; conclusion
d. hypothesis; conditional; conclusion
c. conditional; hypothesis; conclusion
A conditional can have a ____ of true or false.
a. hypothesis
b. truth value
c. counter example
c. conclusion
b. truth value
Which choice shows a true conditional with the hypothesis and conclusion identified correctly?
a. Yesterday was Monday if tomorrow is Thursday.
Hypothesis: Tomorrow is Thursday.
Conclusion: Yesterday was Monday.
b. If tomorrow is Thursday, then yesterday was Tuesday.
Hypothesis: Yesterday was Tuesday.
Conclusion: Tomorrow is not Thursday.
c. If tomorrow is Thursday, then yesterday was Tuesday.
Hypothesis: Yesterday was Tuesday.
Conclusion: Tomorrow is Thursday.
d. Yesterday was Tuesday if tomorrow is Thursday.
Hypothesis: Tomorrow is Thursday. Conclusion: Yesterday was Tuesday.
d. Yesterday was Tuesday if tomorrow is Thursday.
Hypothesis: Tomorrow is Thursday. Conclusion: Yesterday was Tuesday.
What is the conclusion of the following conditional?
A number is divisible by 3 if the sum of the digits of the number is divisible by 3.
a. The number is odd.
b. The sum of the digits of the number is divisible by 3.
c. If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.
d. The number is divisible by 3.
d. The number is divisible by 3.
What is the converse of the following conditional?
If a point is in the first quadrant, then its coordinates are positive.
a. If a point is in the first quadrant, then its coordinates are positive.
b. If a point is not in the first quadrant, then the coordinates of the point are not positive.
c. If the coordinates of a point are positive, then the point is in the first quadrant.
d. If the coordinates of a point are not positive, then the point is not in the first quadrant.
c. If the coordinates of a point are positive, then the point is in the first quadrant.
What is the converse and the truth value of the converse of the following conditional? If an angle is a right angle, then its measure is 90.
a. If an angle is not a right angle, then its measure is 90.
False
b. If an angle is not a right angle, then its measure is not 90.
True
c. If an angle has measure 90, then it is a right angle.
False
d. If an angle has measure 90, then it is a right angle.
True
d. If an angle has measure 90, then it is a right angle.
True
For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional.
If x = 3, then x2 = 9.
a. If x2 = 9, then x = 3. True; x2 = 9 if and only if x = 3.
b. If x2 = 3, then x = 9. False
c. If x2 = 9, then x = 3. True; x = 3 if and only if x2 = 9.
d. If x2 = 9, then x = 3. False
d. If x2 = 9, then x = 3. False
Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional. If either is false, give a counterexample.
If two lines are parallel, they do not intersect.
If two lines do not intersect, they are parallel.
a. One statement is false. If two lines do not intersect, they could be skew..
b. One statement is false. If two lines are parallel, they may intersect twice.
c. Both statements are true. Two lines are parallel if and only if they do not intersect.
d. Both statements are true. Two lines are not parallel if and only if they do not intersect.
a. One statement is false. If two lines do not intersect, they could be skew..
Determine whether the conditional and its converse are both true. If both are true, combine them as a biconditional. If either is false, give a counterexample.
If an angle is a right angle, its measure is 90.
If an angle measure is 90, the angle is a right angle.
a. One statement is false. If an angle measure is 90, the angle may be a vertical angle.
b. One statement is false. If an angle is a right angle, its measure may be 180.
c. Both statements are true. An angle is a right angle if and only if its measure is 90.
d. Both statements are true. The measure of angle is 90 if and only if it is not a right angle.
c. Both statements are true. An angle is a right angle if and only if its measure is 90.
When a conditional and its converse are true, you can combine them as a true ____. a. counterexample
b. biconditional
c. unconditional
d. hypothesis
b. biconditional
Decide whether the following definition of perpendicular is reversible. If it is, state the definition as a true biconditional.
Two lines that intersect at right angles are perpendicular.
a. The statement is not reversible.
b. Reversible; if two lines intersect at right angles, then they are perpendicular.
c. Reversible; if two lines are perpendicular, then they intersect at right angles.
d. Reversible; two lines intersect at right angles if and only if they are perpendicular.
d. Reversible; two lines intersect at right angles if and only if they are perpendicular.
Is the statement a good definition? If not, find a counterexample.
A square is a figure with two pairs of parallel sides and four right angles. a. The statement is a good definition.
b. No; a rhombus is a counterexample.
c. No; a rectangle is a counterexample.
d. No; a parallelogram is a counterexample.
c. No; a rectangle is a counterexample.
One way to show that a statement is NOT a good definition is to find a ____.
a. converse
b. conditional
c. biconditional
d. counter example
d. counter example
Which statement provides a counterexample to the following faulty definition? A square is a figure with four congruent sides.
a. A six-sided figure can have four sides congruent.
b. Some triangles have all sides congruent.
c. A square has four congruent angles.
d. A rectangle has four sides.
a. A six-sided figure can have four sides congruent.
Which biconditional is NOT a good definition?
a. A whole number is odd if and only if the number is not divisible by 2.
b. An angle is straight if and only if its measure is 180.
c. A whole number is even if and only if it is divisible by 2.
d. A ray is a bisector of an angle if and only if it splits the angle into two angles.
d. A ray is a bisector of an angle if and only if it splits the angle into two angles.
Name the Property of Equality that justifies the statement:
If p = q, then p-r = q-r.
a. Reflexive Property
b. Multiplication Property
c. Symmetric Property
d. Subtraction Property
d. Subtraction Property
Which statement is an example of the Addition Property of Equality?
a. If p = q then p x s = q x s.
b. If p = q then p + s = q + s.
c. If p = q then p - s = q - s.
d. p = q
b. If p = q then
Write the converse of the statement. If the converse is true, write true; if not true, provide a counterexample.
If x = 4, then x2 = 16.
If x2 = 16, then x = 4. False; if x2 = 16, then x can be equal to -4.
Write the converse of the given true conditional and decide whether the converse is true or false. If the converse is true, combine it with the conditional to form a true biconditional. If the converse is false, give a counterexample.
If the probability that an event will occur is 0, then the event is impossible to occur.
If an event is impossible, the probability of the event is 0.
True
An event is impossible if and only if the probability of the event is zero.
a. Write the following conditional in if-then form.
b. Write its converse in if-then form.
c. Determine the truth value of the original conditional and its converse. Explain why each of them is true or
false, and provide a counterexample(s) for any false statement(s).
On a number line, the points with coordinates -2 and 5 are 7 units apart.
a. If points have coordinates -2 and 5, then they are 7 units apart.
b. If points are 7 units apart, then they have coordinates -2 and 5.
c. The original conditional is true by the Ruler Postulate. The converse is false. The points 0 and 7 and 7 units
apart, but their coordinates are not -2 and 5.
Write the two conditional statements that form the given biconditional. Then decide whether the biconditional is a good definition. Explain.
Three points are collinear if and only if they are coplanar.
If three points are collinear, then they are coplanar.
If three points are coplanar, then they are collinear.
The biconditional is not a good definition. Three coplanar points might not lie on the same line.
Give a convincing argument that the following statement is true.
If two angles are congruent and complementary, then the measure of each is 45.
If two angles are congruent and complementary, they have equal measures that add to 90. Thus, each angle has a measure that is one-half of 90, or 45.
Write the two conditional statements that make up the following biconditional.
I drink juice if and only if it is breakfast time.
a. I drink juice if and only if it is breakfast time.
It is breakfast time if and only if I drink juice.
b. If I drink juice, then it is breakfast time. If it is breakfast time, then I drink juice.
c. If I drink juice, then it is breakfast time. I drink juice only if it is breakfast time.
d. I drink juice.
It is breakfast time.
b. If I drink juice, then it is breakfast time. If it is breakfast time, then I drink juice.
One way to show that a statement is NOT a good definition is to find a ____. a. counterexample b. biconditional
a. Counter example
Reflexive Property
a = a
Transitive Property
If a = b and b = c, then a = c
Symmetric Property
If a = b then b = a
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