Download 2.1-2.3 Review I. Determine if the conjectu

Name: ___________________________________________________________ Period: __________
2.1-2.3 Review
I. Determine if the conjecture is true or false based on the given information.
1. Given: A rectangle with a perimeter of 16.
Conjecture: A rectangle has the area of 16.
2. Given: points A, B and C
Conjecture: A, B, and C are noncollinear
3. Given: The sides of △ XYZ equal 13.
Conjecture: The side lengths are 3, 4 and 6.
II. Rewrite the statement in if-then form and give the Venn Diagram.
4. Every right angle has an angle with a measure of 90 degrees.
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5. All right triangles have an angle with a measure of 90 degrees.
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III. State whether the following is converse, inverse, contrapositive or none.
If two lines are parallel, then they do not intersect.
6. _______________ If two lines are not parallel, then they do not intersect.
7. _______________ If two lines do not intersect, then they are parallel.
8. _______________ If two lines intersect, then they are not parallel.
9. _______________ If two lines do not intersect, then they are not parallel.
10. ______________ If two lines are not parallel, then they do intersect.
11. Identify the hypothesis and conclusion of the statement: If you’re there before it’s over, then you’re on time.
H: ___________________________________________ C: ________________________________________
12. Write the converse of the statement. If yesterday was Monday, then today is Tuesday.
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13. Identify the inverse of the statement: A square has four sides.
a) If a figure is a square, then it has four sides.
b) If a figure does not have four sides, then it is not a square.
c) If a figure is not a square, then it does not have four sides.
d) If a figure has four sides, then it is a square.
14. Identify the inverse of the statement: A lines contains at least two points.
a) If a figure is not a line, then it does not contain two points.
b) If a figure contains two points, then it is a line.
c) If a figure is a line, then it contains two points.
d) If a figure does not contain two points, then it is not a line.
15. Write the inverse of the statement: A triangle has three sides. Determine if the inverse is true or false. If
false, give a counterexample.
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16. Write the inverse of the statement: Two points on the same line are collinear. Determine if the inverse is
true or false. If false, give a counterexample.
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17. Identify the contrapositive of the statement: Two congruent angles have the same measure.
a) If two angles have the same measure, then they are congruent.
b) If two angles do not have the same measure, then they are not congruent.
c) If two angles are not congruent, then they do not have the same measure.
d) If two angles are congruent, then they have the same measure.
18. Identify the contrapositive of the statement: A square has four congruent angles.
a) If a figure is not a square, then it does not have four congruent angles.
b) If a figure is a square, then it has four congruent angles.
c) If a figure has four congruent angles, then it is a square.
d) If a figure does not have four congruent angles, then it is not a square.
19. Write the contrapositive of the statement: Perpendicular lines form four right angles. Determine if the
contrapositive is true or false. If false, give a counterexample.
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20. Write the contrapositive of the statement: An obtuse angle is greater than 90 degrees.. Determine if the
contrapositive is true or false. If false, give a counterexample.
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21. Use the true statement below and the given information to draw a conclusion. Write that conclusion.
True statement: A bisector of a line segment intersects the segment at its midpoint.
Given: AB bisects CE at D.
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22. Give a valid conclusion that can be reached from statements (1) and (2).
(1) If an angle is acute, then it measure less than 90 degrees.
(2) If an angle measure less than 90 degrees, then it is not obtuse.
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IV. Determine if statement (3) follows from statements (1) and (2). If it does, state which law was used, if not,
write invalid.
23. (1) If you are not satisfied with a DVD, then you can return it within a week for a full refund.
(2) Jen is not satisfied with a DVD.
(3) Jen can return the DVD within a week for a full refund.
24. (1) If x is a real number, then x is an integer.
(2) X is an integer.
(3) X is a real number
25. (1) If fossil fuels are burned, then acid rain is produced.
(2) If acid rain is produced, then wildlife suffers.
(3) If fossil fuels are burned, then wildlife suffers.
V. List the hypothesis and conclusion in each statement.
26. If Susie walks, then she will be late.
27. If Sam does not fail geometry, then he will be eligible to play.
28. Two integers whose sum is 7 cannot both be even.
29. Two angles have equal measure if they are vertical angles.
30. Two opposite rays form a straight line.
31. x >0 whenever x ≠ 0 .
VI. Draw a Venn Diagram, then express each statement in if-then form.
32. Every multiple of 4 is a multiple of 2.
33. When a – b is a positive number, b is less than a.
34. Warren will sing, provided Steve will play the piano.
35. Each angle of an equilateral triangle has measure of 60 degrees.
VII. Write the (a) converse (b) inverse (c) contrapositive for the following exercises.
36. r s
a) __________________ b) __________________ c) __________________
37. t ~u
a) __________________ b) __________________ c) __________________
38. ~v w
a) __________________ b) __________________ c) __________________
39. ~y ~z
a) __________________ b) __________________ c) __________________
40. If it snows, then the game will be postponed.
a) ________________________________________________________________________________
b) ________________________________________________________________________________
c) ________________________________________________________________________________
41. If I save my allowance, then I can go to the movie.
a) ________________________________________________________________________________
b) ________________________________________________________________________________
c) ________________________________________________________________________________
Not only should you use this as a study guide, but look over ALL your notes, quizzes and homework.
Answers
1) false, A=12, l=6, w=2
2) false, A, B, C are collinear
3) false, lengths could be 2, 5, 6
16) If 2 points aren’t on the same
line, then they are not collinear.
17) B
4) If an angle is a right angle, then its
measure is 90 degrees.
5) If a triangle is right, then it has an
angle measure of 90 degrees.
6) none
7) converse
8) contrapositive
9) none
10) inverse
11) H: you’re there before it’s over
C: you’re on time
12) If today is Tuesday, then
yesterday was Monday.
18) D
19) If lines do not form 4 right angles,
then they are not perpendicular
20) If an angle isn’t greater than
90 degrees, then it’s not obtuse.
21) D is the midpoint
22) If an angle is acute, then it’s
not obtuse
23) Detachment
24) invalid
25) Syllogism
26) H: Susie walk, C: she’ll be late
27) H: Sam doesn’t fail geometry
13) C
C: he will be eligible to play
14) A
28) H: 2 integers sum is 7
15) If a figure is not a triangle, then
C: they cannot both be even.
it does not have three sides. TRUE
29) H: angles are vertical
C: they have equal measure
30) H: rays are opposite
C: it forms a straight line
31) H: x ≠ 0 C:
x >0
32) If a number is a multiple of 4,
then it’s a multiple of 2.
33) If a-b is a positive #, then b is
less than a
34) If Steve plays the piano, then
Warren will sing.
35) If a figure is an equilateral triangle,
then each angle has a measure of 60
36) sr, ~r~s, ~s~r
37) ~ut, ~tu, u~t
38) w~v, v~w, ~wv
39) ~z~y, yz, zy
40) If a game is postponed, then it
snowed. If it doesn’t snow, then the
game is not postponed. If the game is not
postponed, then it didn’t snow.
41) If I can go to the movies, then I’ll
save my allowance. If I don’t save my
allowance then I can’t go to the movies.
If I can’t go to the movies, then I didn’t
save my allowance.