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Mid-Term After School Review Sheet #2:
Logic, Properties and Laws
Date: _______________________
Math 10R Period _______
Topic: Logic
Conjunction = AND
Disjunction = OR
Conditional = If --- then --Biconditional = --- if and only if ---Inverse: Negate
Converse: Flip
Contrapositive: Flip and negate
The contrapositive of a conditional is always logically equivalent to the original conditional.
Practice:
1. What is the contrapositive of the statement “If I study, then I pass the test”?
(1) I pass the test if I study.
(2) If I do not study, then I do not pass the test.
(3) If I do not pass the test, then I do not study.
(4) If I pass the test, then I study.
2. Which statement is logically equivalent to “If it is Saturday, then I am not in school”?
(1) If I am not in school, then it is Saturday.
(2) If it is not Saturday, then I am in school.
(3) If I am in school, then it is not Saturday.
(4) If it is Saturday, then I am in school.
3. Which statement is logically equivalent to “If I did not eat, then I am hungry”?
(1) If I am not hungry, then I did not eat.
(2) If I did not eat, then I am not hungry.
(3) If I am not hungry, then I did eat.
(4) If I am hungry, then I did eat.
4. Which statement is logically equivalent to the statement “If you are an elephant, then you do not forget”?
(1) If you do not forget, then you are an elephant.
(2) If you do not forget, then you are not an elephant.
(3) If you are an elephant, then you forget.
(4) If you forget, then you are not an elephant.
5. Given the true statement: “If a person is eligible to vote, then that person is a citizen.” Which statement
must also be true?
(1) Kayla is not a citizen; therefore, she is not eligible to vote.
(2) Juan is a citizen; therefore, he is eligible to vote.
(3) Marie is not eligible to vote; therefore, she is not a citizen.
(4) Morgan has never voted; therefore, he is not a citizen.
6. Which statement is the converse of “If the sum of two angles is 180°, then the angles are supplementary”?
(1) If two angles are supplementary, then their sum is 180°.
(2) If the sum of two angles is not 180°, then the angles are not supplementary.
(3) If two angles are not supplementary, then their sum is not 180°.
(4) If the sum of two angles is not 180°, then the angles are supplementary.
7. What is the converse of the statement "If x is an even integer, then ( x  1) is an odd integer"?
(1) x is not an even integer if and only if ( x  1) is not an odd integer.
(2) x is an even integer if and only if ( x  1) is an odd integer.
(3) If ( x  1) is not an odd integer, then x is not an even integer.
(4) If ( x  1) is an odd integer, then x is an even integer.
8. What is the converse of the statement "If Alicia goes to Albany, then Ben goes to Buffalo"?
(1) If Alicia does not go to Albany, then Ben does not go to Buffalo.
(2) Alicia goes to Albany if and only if Ben goes to Buffalo.
(3) If Ben goes to Buffalo, then Alicia goes to Albany.
(4) If Ben does not go to Buffalo, then Alicia does not go to Albany.
9. What is true about the statement “If two angles are right angles, the angles have equal measure” and its
converse “If two angles have equal measure then the two angles are right angles”?
(1) The statement is true but its converse is false.
(2) The statement is false but its converse is true.
(3) Both the statement and its converse are false.
(4) Both the statement and its converse are true.
10. Given the statement: “If two lines are cut by a transversal so that the corresponding angles are congruent,
then the lines are parallel.” What is true about the statement and its converse?
(1) The statement and its converse are both true.
(2) The statement and its converse are both false.
(3) The statement is true, but its converse is false.
(4) The statement is false, but its converse is true.
11. Given the statement: "A right angle measures 90°." How is this statement written as a biconditional?
(1) If an angle is a right angle, then it measures 90°.
(2) An angle is a right angle if, and only if, it measures 90°.
(3) An angle measures 90° and it is a right angle.
(4) If an angle does not measure 90°, then it is not a right angle.
12. What is the inverse of the statement “If Mike did his homework, then he will pass this test”?
(1) If Mike passes this test, then he did his homework.
(2) If Mike does not pass this test, then he did not do his homework.
(3) If Mike does not pass this test, then he only did half his homework.
(4) If Mike did not do his homework, then he will not pass this test.
13. What is the inverse of the statement “If Julie works hard, then she succeeds”?
(1) If Julie succeeds, then she works hard.
(2) If Julie does not succeed, then she does not work hard.
(3) If Julie works hard, then she does not succeed.
(4) If Julie does not work hard, then she does not succeed.
14.
(1)
(2)
(3)
(4)
What is the inverse of the statement "If Bob gets hurt, then the team loses the game"?
If the team loses the game, then Bob gets hurt.
Bob gets hurt if the team loses the game.
If the team does not lose the game, then Bob does not get hurt.
If Bob does not get hurt, then the team does not lose the game.
15. A conditional statement is always logically equivalent to its
(1) contrapositive
(3) conjunction
(2) converse
(4) inverse
16. Write a statement that is logically equivalent to the statement “If two sides of a triangle are congruent, the
angles opposite those sides are congruent.” Identify the new statement as the converse, inverse, or
contrapositive of the original statement.
17. What is the negation of the sentence: I like ice cream or like pie?
18. What is the negation of sentence: I will go for a run and I will eat healthy?
Topic: Law and Properties
Review your reasons sheet and make sure you know:
Reflexive Property
Symmetric Property
Transitive Property
A quantity is congruent (equal) to itself. a = a
If a = b, then b = a.
If a = b and b = c, then a = c.
Topic: Points, Lines and Planes
Practice:
1. Line k is drawn so that it is perpendicular to two distinct planes, P and R. What must be true about planes P
and R?
(1) Planes P and R are skew.
(2) Planes P and R are parallel.
(3) Planes P and R are perpendicular.
(4) Plane P intersects plane R but not perpendicular to plane R.
2. When two lines intersect, what does their intersection form?
3. When two planes intersect, what does their intersection form?
4. When a line and a plane intersect, what does their intersection form?
5. If two planes are perpendicular to the same line, what can you conclude about the planes?
6. What is the difference between concave and convex?
Review from Review Sheet 1:
1. Which equation represents a line that is parallel to the line y  4 x  5?
1
1
(1) y  4 x  3
(2) y  x  3
(3) y   x  5
(4) y  4 x  5
4
4
2. What is the slope of a line perpendicular to the line whose equation is 5x  3 y  8 ?
5
3
3
5
(1)
(2) 
(3)
(4) 
3
5
5
3
3. Find the slope of a line that passes through the points (5, -8) and (-3, 3)
4. What is the midpoint of the line segment that joins points (4,2) and ( 2,5) ?
3
7
3
3
(1) (1, )
(2) (1, )
(3) ( ,3)
(4) (2, )
2
2
2
2
5. The endpoints of PQ are P(-3,1) and Q(4,25). Find the length of PQ.
6. 12. The midpoint M of line segment AB has coordinates (-3,4). If point A is the origin, (0,0), what are the
coordinates of point B?
7. What is the length of the line segment that joins the points whose coordinates are (4,7) and ( 3,5) ?
(1)
5
(2)
193
(3)
53
(4) 3 6
8. Triangle ABC is formed by the points A(-3, 12), B(6, 2) and C(0, -6). Find the centroid of the triangle.