Download 1 Semester Final Study Guide

CHAPTER
1
1st Semester Final Study Guide
It is in your best interest to do all of the problems and show all of the work
Circle the best answer.
Use the figure for Exercises 1–4.
6. Given LM  MP, which of the following is
always true?
F LM  MP
G M is the midpoint of LP.
H M bisects LP.
J L, M, and P are collinear.
7. Find mLMQ.
1. Which is a name for the plane containing
point D?
A plane DB
C plane EBD
B plane P
D plane FDE
2. Which segment is on plane P but is NOT
on line n?
F BE
H BC
G GB
J AC
A 68°
C 112°
B 90°
D 158°
8. XZ bisects WXY, and mWXY  180°.
What is mZXY?
F 45°
H 135°
G 90°
J 180°
9. Which angles are adjacent but do NOT
form a linear pair?
3. Which names a pair of opposite rays?
A AB and BG
C AB and BA
B BC and AB
D BD and BE
4. Name the intersection of the two planes.
F line n
H line m
G point B
J AC
5. R, S, and T are collinear, and S is between
R and T. If RS  x  1, ST  2x  2, and
RT  5x  5, find RT.
A 2
C 5
B 3
D 6
A 1 and 5
C 2 and 4
B 2 and 3
D 4 and 5
CHAPTER
1
1st Semester Final Study Guide
10.The measure of A is twice the measure of
its complement. What is the measure of A?
F 20°
H 60°
G 30°
J 90°
11. If mB  (180  x)°, what is the
measure of a supplement of B?
17. Given a right triangle with the length
of one leg equal to 9 centimeters and the
length of the hypotenuse equal to
15 centimeters, what is the length of
the other leg?
A 180°
C (180  x)°
F 6 cm
H
B x°
D (90  x)°
G 12 cm
J 144 cm
12. What is the length of a rectangle if the
perimeter is 88 inches and the length is 2
inches more than the width?
F 21 in.
H 25 in.
G 23 in.
J 42 in.
306 cm
18. What transformation is shown?
13. What is the height of a triangle with an
area of 16.5 square meters if the base
is 5.5 meters?
A 1.5 m
C 6 m2
B 3m
D 6m
14. A circle has an area of 81 square feet.
What is its radius?
F 9 ft
G 9 ft
H 20.5 ft
2
J 40.5 ft
15. Given GH with endpoints G(7, 3) and
H(7, 11), what are the coordinates of the
midpoint of GH ?
A (0, 4)
C (7, 7)
B (0, 8)
D (14, 14)
16. What is the distance from M(9, 4) to
N(1, 2)?
A
10
B 10
C 2 26
D 12
A rotation
C translation
B reflection
D image
CHAPTER
2
1st Semester Final Study Guide
Circle the best answer.
1. What is the next item in the pattern?
6. Given: Three noncollinear points lie on
the same plane. A student makes a
three-legged stool. What conclusion can
be drawn?
F The stool will wobble.
A
C
G The stool will fall over.
B
D
H The stool will not wobble.
J No conclusion can be drawn.
2. Which conjecture is NOT always true?
F Intersecting lines form 4 pairs of
adjacent angles.
G Intersecting lines form 4 pairs of
linear adjacent angles.
H Intersecting lines form 4 pairs of
congruent angles.
J Not here
3. Given the conditional statement “The
counting number 0 is an integer,” what
can be concluded?
7. If the number formed by the last two
digits of a larger number is divisible by 4,
then the larger number is divisible by 4. If
a number is divisible by 4, then it is
divisible by 2. What conclusion can be
drawn about the numbers if its last two
digits are 92?
A Only the smaller number is divisible
by 2.
B Both numbers are divisible by 2.
A The statement is false because the
hypothesis is false.
C Only the larger number is divisible
by 2.
B The statement is false because the
conclusion is false.
D No conclusion can be drawn.
C The statement is false because both
the hypothesis and the conclusion
are false.
D The statement is true.
4. Which is NOT a counterexample for the
conditional statement “If x  0, then
1
 x”?
x
1
F 2
H
2
G 1
J 2
5. Let p represent “B is between A and C”
and q represent “A, B, and C are
collinear.” Which symbolic statement
represents the conditional statement
“If B is not between A and C, then
A, B, and C are not collinear”?
A pq
C
p
B qp
D p
q
q
8. Which conditional statement can be used
to write a true biconditional?
F If a figure is a square, then it is a
rectangle.
G If the product is odd, then both
factors are odd.
H If two angles form a linear pair, then
they are adjacent.
J If two angles are supplementary,
then both angles are obtuse.
9. Suppose that m1  mA, and mA 
34. What can you conclude by using the
Transitive Property of Equality ?
A 34  mA
C mA  mA
B mA  m1
D m1  34
CHAPTER
2
1st Semester Final Study Guide
10. Which could NOT be used to justify
1  2?
F Trans. Prop. of 
G Reflex. Prop. of 
H Sym. Prop. of 
J Def. of 
12. Which is NOT a reason for
Steps 2, 6, 7, or 8?
F Add. Post.
H Def. of rt. 
Use the partially completed twocolumn proof for Exercises 11 and 12.
Use the two-column proof for
Exercises 13 and 14.
Given: X is in the interior of ABC, ABC
is a right angle, and mXBC  45.
Given: 1 and 2 are complementary and
1  3.
Prove: 2 and 3 are complementary.
Prove: BX bisects ABC.
Proof:
Statements
Reasons
1. X is in the interior of
ABC.
1. Given
2.
2.
?
?
3. ABC is a right angle. 3. Given
4.
?
4.
?
5. mXBC  45
5. Given
6.
6. Subst.
?
7. mABX  45
7.
?
8.
8.
?
?
9. BX bisects ABC.
9. Def. of
bisector
11. Which is NOT a statement for
Steps 2, 4, 6, or 7?
A mABX  45°  90
B mABC  mABX  mXBC
C mABC  90
D ABX  XBC
G Subtr. Prop. of 
J Def. of  s
Two-Column Proof:
Statements
Reasons
1. 1 and 2 are
complementary.
1. Given
2. (a)
2. Def. of  s
3. 1  3
3. Given
4. m1  m3
4. Def. of 
5. m2  m3  90°
5. Subst.
6. 2 and 3 are
complementary.
6. (b)
13. In the proof, what belongs in the space
labeled “a”?
A m3  m2  90°
B 1  3
C m1  m2  90°
D m1  m3
14. In the proof, what belongs in the space
labeled “b”?
F Def. of comp. s
G Subst.
H Def. of  s
J  Add. Post.
CHAPTER
1st Semester Final Study Guide
3
Circle the best answer.
1. Classify HG and AD.
5. Which correctly completes the sentence?
When two lines are parallel, the acute
angles they form with a transversal are
________ to the obtuse angles.
A supplementary
B complementary
C congruent
A skew segments
B parallel segments
C perpendicular segments
D vertical
Use the figure for Exercises 6 and 7.
D intersecting segments
2. If lines and m are skew, how many
planes contain two points of both lines?
F 0
H 2
G 1
J 3
3. Which are NOT alternate interior angles?
6. Given r || s  p, which angle is NOT
congruent to 4?
F 2
H 5
G 3
J 6
7. Given r  s  p, what is the measure of
1?
A 3 and 6
C 2 and 3
A 40°
C 110°
B 2 and 7
D 4 and 5
B 90°
D 140°
4. The angles formed by two lines and a
transversal are labeled 1 through 8. If 1
and 8 are alternate interior angles and
1 and 5 are vertical angles, what type
of angle pair is 5 and 8?
8. Which CANNOT be used to prove that
lines m and n are parallel?
F alternate exterior angles
G corresponding angles
F 2  4
H alternate interior angles
G 4 is supplementary to 7.
J same-side interior angles
H 4 is supplementary to 5.
J 1  5
9. Lines r and s are cut by a transversal
so that 1 and 2 are same-side
interior angles. If m1  (8x  40)°
and m2  (12x  20)°, for what value of
x is it true that r  s?
A 6
C 30
B 10
D 60
CHAPTER
1st Semester Final Study Guide
3
10. If a transversal is perpendicular to one of
two parallel lines, which statement is
NOT correct?
13. Which is the justification for Step 5?
A 2 lines  to same line  2 lines 
F All the angles formed are congruent.
B 2 intersecting lines form linear pair of
 /s  lines 
G Every pair of angles is supplementary.
C  Transv. Thm.
H The transversal is  to the other line.
J Every pair of angles is complementary.
11. Which is a possible value of x?
A 21
C 25
B 23
D 26
Use the figure and the partially
completed proof for Exercises 12 and 13.
D Same-Side Interior Angles Theorem
14. Given the point J(2, 4), for which point
K is JK a line with undefined slope?
F K(2, 4)
H K(4, 2)
G K(2, 4)
J K(2, 4)
15. Given points A(1, 4), B(0, 4), C(2, 0),
and D(2, 5), what type of lines are AB
and CD ?
F parallel
H horizontal
G perpendicular
J vertical
16. Which is an equation of a horizontal line?
A x3
Given: AC is the shortest segment from A to
CD and m1  m2.
Prove: AB  AC
Statements
Reasons
1. m1  m2
1. Given
2. ___?___
2. Given
3. AC  CD
3. Distance from a
point to a line
4.
4. Conv. of Alternate
Int. /s Thm.
5. AB  AC
B y  4
D y  x
17. Which is the equation of a line that does
NOT go through the origin?
F x0
H yx
G yx1
J y  2x
18. Which line is NOT parallel to y 
Proof:
?
C yx
5.
?
12. Which is the statement for Step 2?
F AB || CD
H AC  CD
G BD  CD
J Not here
A 2x  3y  6
2
x 2?
3
C 6y  12  4x
1
1
y  x 1
D 4x  6y  12
2
3
19. Which of the following is the equation of
the line that passes through (2, 1) and is
perpendicular to 5x  y  9?
B
F x  5y  3
G y  5 x 
H x  5y  3
3
5
J y  5x 
3
5
CHAPTER
1st Semester Final Study Guide
4
Circle the best answer.
1. Which best describes ABC with
vertices A(2, 1), B(0, 4), and C(2, 1)?
A acute
C obtuse
B equiangular
D right
2. Which is a correct classification of DEF
with vertices D(3, 2), E(2, 3), and
F(1, 0)?
F equilateral
H scalene
G isosceles
J Not here
3. If the acute angles of a right triangle are
congruent, which statement is NOT true?
A Both acute angles measure 45.
B Only one exterior  measures 90.
C Only one exterior  measures 135.
D Two exterior angles measure 135.
4. What is the value of x?
F 41
H 99
G 58
J 122
5. QRS  STQ, QS  x  10 and
SQ  2x  2. What is the value of x?
2
A 4
C 2
B 2
D 4
6. ABC  DEF. What information is NOT
needed to find the perimeter of ABC if
you are given all four lengths below?
F DE
H CF
G BG
J EF
Use the partially completed two-column
proof for Exercise 7.
Given:
Prove: GHF  MOL
Proof:
Statements
1. GF  ML,
Reasons
1. Given
FH  LO,
GH  MO
2. F  L
2.
3. H  O
3. Given
4. G  M
4.
?
5. GHF  MOL
5.
?
?
7. Which reason does NOT belong in the
proof?
A Def. of  s
B Third s Thm.
C Rt.   Thm.
D CPCTC
Use the figure for Exercises 8–11.
8. AB  y  3, DC  3y  1,
EB  3y  1, ED  y  1, AE  y,
CE  2y. What value of y proves
AEB  CED by the SSS Postulate?
F 2
H 1
G 1
J 2
CHAPTER
1st Semester Final Study Guide
4
9.
What information would allow you to
prove AED  CEB by SAS?
A E is the midpoint of DB .
B E is the midpoint of AC .
Use the partially completed twocolumn proof for Exercises 13 and 14.
Given: JK  LK ; JYL and LXJ are rt. s
.
C E bisects AC .
D E bisects both DB and AC .
10. If ADC and ABC are right angles,
AC  BD, and AB  DC, which postulate
or theorem proves ABC CDA?
F SSS
H ASA
G SAS
J HL
11. If AD BC and ABD  CDB,
which postulate or theorem could be
used to prove ABD  CDB?
Prove: JY  LX
Proof:
Statements
Reasons
1. KJL  KLJ
1.
?
2. JL  LJ
2.
?
3. JYL and LXJ
are rt. s .
3. Given
A SAS
C SSS
4. JYL  LXJ
4.
?
B ASA
D HL
5. JYL  LXJ
5.
?
6. JY  LX
6.
?
12. What is mDAC?
13. Which justification belongs in Step 1?
A Isosc.  Thm.
B Reflex. Prop. of 
F 30
H 60
G 45
J Not here
C Rt.   Thm.
D CPCTC
14. Which justification belongs in Step 6?
F Isosc.  Thm. H Rt.   Thm.
G HL
J CPCTC
CHAPTER
1st Semester Final Study Guide
5
Circle the correct answer.
1. AB  18.5, AX  8.1 and BC  18.5. What
is the length of AC ?
A 8.1
B 9.25
C 16.2
5. X is the incenter of NPQ. What MUST
be true?
A KN  KP
C XM  KX
B XN  QX
D NM  QL
6. If G is the centroid of ABC, what MUST
be true?
D 18.5
2. JK has endpoints J(1, 3) and K(3, 5).
The intersection of JK and its
perpendicular bisector is (2, 4). Which is
the equation for the perpendicular
bisector of JK ?
A y  4  1(x  2)
B y  4  1(x  2)
A FG  EG
7. The orthocenter of a triangle is the point
of concurrency of which lines?
C y  5  1(x  3)
A altitudes
D y  5  1(x  3)
B angle bisectors
3. What is true about DEY and FEY?
2
B CG  CD
3
C medians
D perpendicular bisectors
8. A midsegment connecting two sides of a
triangle is parallel to the third side and
equal to which measurement?
A 2 times the third side
A mDEY  mFEY  90°
B mDEY  mFEY
4. Which is equidistant from the vertices
of a triangle?
B
1
times the third side
2
9. CA is a midsegment of VTU. What is
the measure of BCA?
A circumcenter
B incenter
A 40°
B 50°
CHAPTER
5
1st Semester Final Study Guide
continued
10. Which statement contradicts the
statement that RST is a right
triangle?
14. What is the value of x?
A mR  90°
B R and T are complementary.
C S is obtuse.
A 13
D R  T
B 17
11. Which inequality best describes the
possible lengths of the third side of a
triangle with two sides of lengths 11
and 9?
A 9  s  11
B 11  s  9
C 2  s  20
D 2  s  20
Use the figures for Exercises 12 and
13.
C 119
D 169
15. Which number forms a Pythagorean
triple with 8 and 10?
A 6
B 15
16. What is the classification of ABC with
side lengths 7, 11, and 13?
A acute
B obtuse
17. What is the value of x?
12. Which shows the angles of FED in
order from smallest to largest?
A D, E, F
A 2 8
B F, D, E
B 8
C E, F, D
C 8 2
D D, F, E
D 128
13. Compare E and H.
18. What is the value of y?
A H  E
B E  H
A 3 4
B 4
C 4 3
D 8
Name _______________________________________ Date ___________________ Class __________________
CHAPTER
1st Semester Final Study Guide
6
Circle the best answer.
6. WXYZ is a parallelogram. What is the
value of x?
1. Which term does NOT describe the
figure?
A 7
B 10
7. Which MUST be a parallelogram?
A concave
C polygon
B hexagon
D regular
2. What is the sum of the measures of the
interior angles of a 5-sided convex
polygon?
A 72
C 540
B 360
D 900
A Figure 1
B Figure 2
8. If EF || GH , what additional information
would allow you to conclude that EFGH is
a parallelogram?
3. What is the value of a?
A EF  GH
A 60
B FG  EH
B 80
ABCD intersect at X.
4. The diagonals of
Which is NOT true?
A DAB  BCD
B mDAB  mCBA  180
C BC  AD
D AX  XB
Use the figure for Exercises 5 and 6.
5. WXYZ is a parallelogram. Which is
mW?
A 68
B 112
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
107
Holt Geometry