Unit 4 Test 1 Review
Name:_____________________
Determine the converse, inverse, and contrapositive of the conditional statements. Indicate whether
each statement is true or false.
1. Conditional statement: If R is the midpoint of QS , then QR  RS .
Converse: ________________________________________________________________
Inverse: __________________________________________________________________
Contrapositive: ____________________________________________________________
2.Write a conditional statement from the diagram. Then write
the converse, inverse, and contrapositive. Find the truth value of each.
____________________________________________________________
____________________________________________________________
________________________________________________________________________________________
Tell whether each conclusion uses inductive or deductive reasoning.
3. A sign in the cafeteria says that a car wash is being held on the last Saturday of May. Tomorrow is the last
Saturday of May, so Justin concludes that the car wash is tomorrow.
4. So far, at the beginning of every Latin class, the teacher has had students review vocabulary. Latin class is
about to start, and Jerry assumes that they will first review vocabulary.
Write the final statement and determine whether each conjecture is valid by the Law
of Detachment or Syllogism.
5.Given: If you ride the Titan roller coaster in Arlington, Texas, then you will drop 255 feet.
If you drop 255 feet, then you will be scared.
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6. Given: A segment that is a diameter of a circle has endpoints on the circle.
GH has endpoints on a circle.
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Write a biconditional from each given conditional and converse.
7. Conditional: If two angles share a side, then they are adjacent.
Converse: If two angles are adjacent, then they share a side.
Biconditional: _____________________________________________________________
8. Conditional: If your temperature is normal, then your temperature is 98.6F.
Converse: If your temperature is 98.6F, then your temperature is normal.
Biconditional: _____________________________________________________________
Use the table for Exercises 7-10. Determine if a true biconditional statement can be written from each
conditional. If so, then write a biconditional. If not, then explain why not.
Mountain Bike Races
Characteristics
Cross-country
A massed-start race. Riders must carry their
own tools to make repairs.
Downhill
Riders start at intervals. The rider with the
lowest time wins.
Freeride
Courses contain cliffs, drops, and ramps.
Scoring depends on the style and the time.
Marathon
A massed-start race that covers more than
250 kilometers.
9. If a mountain bike race is mass-started,
then it is a cross-country race.
10. If a mountain bike race is downhill,
then time is a factor in who wins.
________________________________________
________________________________________
________________________________________
________________________________________
11. If a mountain bike race covers more than
kilometers, then it is a marathon race.
12. If a race course contains cliffs, drops, and 250
ramps, then it is not a marathon race.
________________________________________
________________________________________
________________________________________
________________________________________
Identify the property that justifies each statement.
13.If ABC  DEF, then DEF  ABC.
14.1  2 and 2  3, so 1  3.
15.If FG  HJ, then HJ  FG.
16. WX  WX
Write a justification for each step.
17. CE  CD  DE
_________________________
6x  8  (3x  7)
_________________________
6x  15  3x
_________________________
3x  15
_________________________
x5
_________________________
18. mPQR  mPQS  mSQR
______________________________
90  2x  (4x  12)
______________________________
90  6x  12
______________________________
102  6x
______________________________
17  x
______________________________
19. Given: HKJ is a straight angle, KI bisects HKJ.
Prove: IKJ is a right angle.
Statements
Reasons
1. a. ______________________________
1. Given
2. mHKJ  180
2. b._______________________________
3. c. _______________________________
3. Given
4. IKJ  IKH
4. Def. of  bisector
5. mIKJ  mIKH
5. Def. of  s
6. d. ______________________________
6.  Add. Post.
7. 2mIKJ  180
7. e. Subst. (Steps _______)
8. mIKJ  90
8. Div. Prop. of 
9. IKJ is a right angle.
9. f. _______________________________
Identify Relationships
Corresponding
Angles Postulate
If two parallel lines are cut by
a transversal, then the pairs of
corresponding angles are
congruent.
Name the pairs of angles congruent
by the Corresponding Angles Postulate.
1. ___________________________
2. ___________________________
3. ___________________________
4. ___________________________
Alternate Interior
Angles Theorem
If two parallel lines are cut by
a transversal, then the two
pairs of alternate interior
angles are congruent.
Name the pairs of angles congruent
by the Alternate Interior Angles
Theorem.
5. ___________________________
6. ___________________________
Alternate Exterior
Angles Theorem
If two parallel lines are cut by
a transversal, then the two
pairs of alternate exterior
angles are congruent.
Name the pairs of angles congruent
by the Alternate Exterior Angles
Theorem.
7. ___________________________
8. ___________________________
Same-Side Interior
Angles Theorem
If two parallel lines are cut by
a transversal, then the two
pairs of same-side interior
angles are supplementary.
Name the pairs of angles
supplementary by the Same-Side
Interior Angles Theorem.
9. ___________________________
10. ___________________________
Find each angle measure.
20. mABC _______________________
21. mDEF _______________________
Give two examples of each kind of angle pair in the figure.
22. alternate interior angles __________________________
23.alternate exterior angles
__________________________
24.same-side interior angles _________________________
25. Corresponding angles
_________________________
26. Given p q , m1 = 100°, and m2 = 61°, find the measures of all the numbered angles.
m3 = _____, m4 = ______, m5 = ______, m6 = ______
10
m7 = _____, m8 = ______, m9 = ______
11
12
m10 = _____, m11 = ______, m12 = ______
What is the relationship between
1 and 4?
What is the relationship between
2 and 8?
What is the relationship between
6 and 9?
Complete the two-column proof to show that same-side exterior angles are supplementary.
27. Given: p || q
Prove: m1  m3  180
Statements
Reasons
1. p || q
1. Given
2. a. _______________________
2. Lin. Pair Thm.
3. 1  2
3. b. _______________________
4. c. _______________________
4. Def. of  s
5. d. _______________________
5. e. _______________________
Use the figure for Exercises 1–8. Tell whether lines m and n
must be parallel from the given information. If they are, state
your reasoning. (Hint: The angle measures may change for
each exercise, and the figure is for reference only.)
28. 7  3
29. m3(15x22)°, m1(19x  10), x8
________________________________________
30. 7  6
__________________________________________
31. m2(5x3)°, m3(8x  5),
________________________________________
32.m8(6x  1)°, m4(5x3)°, x9
x14
__________________________________________
33. 5  7
________________________________________
__________________________________________
34. In the diagram of the gate, the horizontal bars
are parallel and the vertical bars are parallel.
Find x and y.
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35. A bedroom has sloping ceilings as shown. Marcel is hanging
a shelf below a rafter. If m1(8x  1), m2(6x7),
and x4, show that the shelf is parallel to the rafter above it.
_____________________________________________
36. In the sign, m3(3y7), m4(5y5), and y21.
Show that the sign posts are parallel.
_____________________________________________
Choose the best answer.
37.In the bench, mEFG(4n16), mFJL(3n40),
mGKL(3n22), and n24. Which is a true statement?
A FG || HK by the Converse of the Corr. s Post.
B FG || HK by the Converse of the Alt. Int. s Thm.
C EJ || GK by the Converse of the Corr. s Post.
D EJ || GK by the Converse of the Alt. Int. s Thm.
38. In the windsurfing sail, m5(7c1), m6(9c  1),
m717c, and c6. Which is a true statement?
A RV is parallel to SW .
B SW is parallel to TX .
C RT is parallel to VX .
D Cannot conclude that two segments are parallel
In Exercises 39–42, use the given information to determine the theorem or postulate that proves m || n.
39. 1  7
_______________________________
40. m4m5180
_______________________________
41. 5  3
_______________________________
42. 8  4
_______________________________
Name the shortest segment from the point to the line and write an inequality for x.
42.
44.
________________________________________
________________________________________
Use the drawing of a basketball goal.
In each exercise, justify Esperanza’s conclusion with one
of the completed theorems from Exercises 45–47. Write the
number 45, 46, or 47 in each blank to tell which theorem you used.
45. Esperanza knows that the basketball pole intersects the
court to form a linear pair of angles that are congruent.
She concludes that the pole and the court are perpendicular.
______________________
46.Esperanza knows that the hoop and the court are both
perpendicular to the pole. She concludes that the hoop
and the court are parallel to each other.
______________________
47.Esperanza knows that the hoop and the court are parallel to
each other. She also knows that the hoop is perpendicular to
the pole. Esperanza concludes that the pole and the court
are perpendicular.
______________________
Complete the two-column proof.
49. Given: m  n
Prove: 1 and 2 are a linear pair of congruent angles.
Proof:
Statements
Reasons
1. a. ___________________________
1. Given
2. b. ___________________________
2. Def. of 
3. 1  2
3. c. ___________________________
4. m1m2180
4. Add. Prop. of 5
5. d. ___________________________
5. Def. of linear pair
Apply the transformation M to the polygon with the given vertices. Identify and
describe the transformation.
49. M: (x, y)  (x  2, y  3)
50. M: (x, y)  (x, y)
A(1, 3), B(2, 1), C(2, 4)
P(1, 2), Q(2, 3), R(1, 2)
_____________________________________
____________________________________
51.M: (x, y)  (y, x)
G(4, 3), H(2, 3), J(2, 1), K(4, 1)
52.M: (x, y)  (2x, 2y)
E(2, 2), F(1, 1), G(2, 2)
____________________________________
_____________________________________
Apply the transformation M to the polygon with the given vertices. Name the coordinates of the image
points. Identify and describe the transformation.
53. M(x, y)  (x1, y2)
A(3, 10), B(6, 4), C(1, 4)
____________________
____________________
54. M(x, y)  (
1 1
x, y)
2 2
A(1, 3), B(4, 1), C(2, 1)
____________________
____________________
Determine whether the polygons with the given vertices are congruent. Support your answer by
describing a transformation.
55. E(4, 1), F(2, 1), G(4, 3)
56. K(3, 1), L(1, 8), M(4, 1)
W(1, 3), X(1, 5), Y(7, 7)
T(7.5, 2.5), R(2.5, 20), S(10, 2.5)
____________________
____________________
____________________
____________________
Describe each of the following mapping notations in words and give an example using the
point (3, 2) for (x, y). Assume (0, 0) is the center of the transformation, where appropriate.
57. (x, y)  (x, y)
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58. (x, y)  (x  a, y  b)
_____________________________________
59. (x, y)  (x, y)
_____________________________________
60. (x, y)  (y, x)
_____________________________________
61. (x, y)  (kx, ky), k  0
_____________________________________
62. (x, y)  (y, x)
_____________________________________
63. (x, y)  (x, y)
_____________________________________