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2013-14 Geometry
Semester 1 Final Exam Study Guide Chapter 1
Name_________________________________
FCS, Mr. Garcia
Date___________________
Period______
This is your semester 1 exam review study guide. It is designed for you to do a portion each day until the day of
the exam.
You may use the following formula to calculate your semester grade given an assumed final exam grade.
(Current Re nWeb Grade)x.90 + (semester exam) x .10 = final grade
Topics that we have covered on chapters 1 through 4 are outlined below for your review.
===============================================================================
Chapter 1: Points, Lines, and Planes
Point, line, plane – are undefined terms. They do not need to be defined.
Definitions or defined terms are explained using undefined terms and/or other defined tersms.
Space is defined as a boundless, 3-dimensional set of all points. Space can contain lines and planes.
1. How do you name a line? ______, a line segment? _______, a ray? ________, a plane? __________,
2. an angle, ____________, a triangle ? ________, a quadrilateral? _________, a pentagon?
_________.
3. What does it mean for 3 or more points to be collinear? _______________________________,
Noncollinear? ____________________________________.
4. What does it mean for 3 or more points to be coplanar? _______________________________,
Noncoplanar? _______________________________.
Relationships of lines and planes:
5. What does it mean for 2 lines to be parallel? ______________________________________.
6. What is the symbol for parallel? ______
What is the symbol for perpendicular? ______.
7. When 2 lines intersect, they intersect at a p________________.
8. When a line and a plane intersect, they intersect at a p____________________.
9. When 2 planes intersect, they intersect at a l __________________________.
10. An angle bisector could be a s_________________, a l____________________, or a r____________.
11. Any segment, line, or plane that intersects a segnment at its m_________________ is called a
Segment b______________________.
12. When a line segment, a ray, or a line, bisects a segment, the bisector creates two s__________________
that are equal in m____________________, or equal in l________________.
13. If 2 segments are equal in length, or in measure, then they are said to be c____________________. The
postulate that states this is called? _____________________. Look it up in you textbook.
14. When a line segment, a ray, or a line, bisects an angle, it creates two c__________________ angles, and
their measures are e_________________.
15. What is the difference between an expression and an equation? Write an example of each.
16. A point where the 2 sides of an angle meet is called? v____________.
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2013-14 Geometry
Semester 1 Final Exam Study Guide Chapter 1
FCS, Mr. Garcia
y
17. The slope of a line
can be calculated when you are given 2 p________________.
x
18. What is the slope formula? Look it up in your textbook.
19. The Pythagorean theorem formula and the distance formula are really the same, however you use the
Pythagorean formula, c2 = a2 + b 2 , when you are given 2 d_____________________, and you use the
distance formula, (x2 - x1 )2 + ( y2 - y1 )2 , when you are given 2 p____________. Write 2 example
problems to show their use.
20. The midpoint of a segment is the point halfway between the e______________ of a segment.
x  x y  y2
sum of x ' s sum of y ' s
,
) or ( 1 2 , 1
) , when you are
21. You use the midpoint formula (pg. 27), (
2
2
2
2
given 2 p________________, and you are asked to find the midpoint of a s_______________________.
Create a problem example and solve it.
Find the slope of the line through the given points.
22. A(-3,8), B(4,2) _____
23. What is the slope of any line parallel to the line through points A and B? _____
24. What is the slope of any line perpendicular to the line through points A and B? _____
25. C(1,-3), D(9,-9) _____
26. What is the slope of any line parallel to the line through points C and D? _____
27. What is the slope of any line perpendicular to the line through points C and D? _____
28. E(-2,-3), F(-6,-5) _____
29. What is the slope of any line parallel to the line through points E and F? _____
30. What is the slope of any line perpendicular to the line through points E and F? _____
==============================================================================
Chapter 1-1 exercises. Refer to the figure to the right to answer problems 1 - 7.
X
_______ 1. The line intersecting plane P.
______2. The intersection of AC and XF .
A
B
C
______3. Are points B, F, and X collinear?
______4. Are points A, B, and X coplanar?
______5. Are points A, B, and X contained in Plane P?
D
F
P
____ ____ ____6. Identify 3 non-collinear points
____ ____ ____ ____7. Identify 4 non-coplanar points.
j
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2013-14 Geometry
Semester 1 Final Exam Study Guide Chapter 1
FCS, Mr. Garcia
Use the midpoint theorem and the segment addition property and the distance formula to solve the following
problems.
8. If B is the midpoint of AC and AB = 2x – 3 and BC = 5x – 24, find x, AB, and BC.
X = _____, AB = _____, BC = _____
9. If XB = 14 and XF = 20, find BF. ______
10. If B is the midpoint of XF and XB = x + 11 and BF = 5x – 1, find x and XF. ____, ____
11.
If AB = 3x, BC = x + 2, and AC = 38, find x and AB. _____, _____
12. If the coordinate x of G is –8 and the x coordinate of H is 9, find GH. ______
13. Find the midpoint of the segment having the given endpoints:
a. A(-2, -4), B(3, 8) ______
b. C( 3, -4), D( -3, -1) ______
c. E( 2, 1), F(5, 1)_____
14. Find the distance between the given endpoints:
a. A(-2, -4), B(3, 8) ______
b. C( 3, -4), D( -3, -1) ______
c. E( 2, 1), F(5, 1)_____
d. If the length of PQ is twice the length of AB , then find PQ. _____
e. If the length of RS is one third the length of EF , then find RS. _____
15. Find the coordinates of A, the missing endpoint, if B(-2, 5) is the midpoint of AC , and the coordinates of
C are (-5, 4). See example 5 on page 28.
Also do, Pg. 79-80: 2-22 (even); (more practice exercises).
==============================================================================
Chapter 1-4, Pg. 36 Angle Measure
1. An angle is formed by two noncollinear rays that have a common endpoint. The rays are called
s___________ of the angle. The common endpoint is the v_________________ of the angle and it must
always be in the center of the name of the angle. Angles are measure in d_____________.
2. There 3 types of angles: a r____________ angle; it measures ________________ degrees.
3. An a_______________ angle; it measures < 90 degrees, and an o____________ angle; it measures
_________ degrees.
4. One could say that there is a fourth type of angle called the straight angle, which is just a line made up
of two opposite rays; it measures 180 d__________________.
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2013-14 Geometry
Semester 1 Final Exam Study Guide Chapter 1
FCS, Mr. Garcia
1-5 Angle pair relationships
1. Adjacent angles are 2 angles that have a common v__________ and a common s___________, but no
common interior points. Draw an example of 2 adjacent angles and a counterexample.
2. A linear pair is a pair of adjacent angles with noncommon sides that are opposite r_________.
Draw an example of a linear pair and a counter example.
3. Vertical angles are two nonadjacent angles formed by two intersecting lines.
Draw an example of vertical angles and a counterexample.
4. Complementary angles are two angles, whose m___________________ add up to 180
d________________. Draw an example.
5. Supplementary angles are two angles, whose m___________________ add up to 180
d________________. Draw an example.
6. Perpendicular lines intersect to form f__________ right a________________. Draw a picture that
illustrates this. Add the right angle symbol to your drawing. The symbol of perpendicular is ______.
=============================================================================
Refer to Figure 2. Matching, you may use more than one letter to describe the angle(s).
________ 1.
________ 2.
________ 3.
________ 4.
________ 5.
________ 6.
________ 7.
________ 8.
________ 9.
1 and 2
1 and 5
3 and 4
1 and BOE
1 and 6
AOF and BOE
AOC and COE
2 and 5
4 and AOD
a. acute angles
b. right angles
c. obtuse angles
d. adjacent angles
e. linear pair
f. complementary angles
g. supplementary angles
h. vertical angles
i. congruent angles
C 
D
B
3
2
A

4
1
O

6
E

5
F
G

Figure 2
=============================================================================
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2013-14 Geometry
Semester 1 Final Exam Study Guide Chapter 1
FCS, Mr. Garcia
Refer to figure 2 to solve problems 10 - 17.
10. If m3 = 27, then m4 = _____,
and m1 + mBOD = m_____.
12. If m1 = 46 and m4 = 59, then mDOF = _____.
13. If
OD
bisects COE, then m4 = _____.

C 
D
B
3
2
A

4
1
O
14. If OD  BF , then m4 + m5 = _____.
15. If OD  BF and m4 = 65, then m1 = _____,
and m2 = _____, m6 = _____, mAOF = _____.

6
5
F

G
16. If OD  BF , name all the pairs of complementary angles.______________
_____________________________________________________________
E

Figure 2
17. If OD is the  bisector of BF , which segments are congruent? __________
18. Name the vertex of DOF _____________.
19. Write another name for 6 ________________.
=============================================================================
Refer to figure 3 to solve problems 18 - 21.
20. Given: m2 = 9x +28 and m3 = 47 – 2x, x = _____, m2 = _____
2
1
21. Given: m1 = 3x + 5 and m3 = 65, x = _____
22. Given: m2 = 9x +2 and m4 = 7x + 36, x = _____, m2 = _____
3
4
Figure 3
23. Given: m1 = x-9 and m2 = 2x, x = _____, m1 = _____
Do problems page 80-81: 24 – 30 (even).
1-6 and 1-7 Two and Three Dimensional Figures
1. A polygon is a closed figure formed by a finite number of c_____________ segments called
s___________ such that the sides have a common e_______________ are noncoplanar, and each side
intersects exactly 2 other sides, but only at their e_________________.
2. The vertex of each angle is a vertex of the polygon. A polygon is named by the letters of its
v____________. Written in the order of the consecutive v________________.
3. A polygon can be c_________________ and convex.
4. A polygon with 4 sides is called a q__________________. One with five sides is called a
p_________________. One with n-sides is called an n-gon. In the name Polygon, poly stands for
m__________ and gon stands for s________________.
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2013-14 Geometry
Semester 1 Final Exam Study Guide Chapter 1
FCS, Mr. Garcia
5. An equilateral polygon is a polygon in which all s_____________ are congruent, and an equiangular
polygon is one in which all a______________________ are c______________________.
6. A convex polygon that is both equiangular and e__________________ is called a r______________
polygon.
7. The perimeter of a polygon is the s________ of the lengths of the s____________. The circumference
of a circle is the d_________________ around the circle.
8. The area of a figure is the number of square units needed to cover a s_______________. Review all the
formulas on page 58 in your textbook. Draw the figure and write the formula underneath it.
9. Dasan has 32 feet of fencing to fence in a play area for his dog. Which shape of play area uses the modt
or all of the fencing and encloses the largest area?
a.
b.
c.
d.
Circle with radius of about 5 feet
Rectangle with length 5 feet and width 10 feet
Right triangle with legs of length 10 feet each
Square with side length 8 feet
10. Find the perimeter and area of
ABC with vertices A(-1, 4), B(-1, -1), and C(6, -1).
11. A rectangle of area 360 sq. meters is 10 times as long as it is wide. Find its length and width.
12. The vertices of a rectangle with side lengths of 10 and 24 units are on a circle of radius 13 units. Find
the area between the figures.
13.
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2013-14 Geometry
Semester 1 Final Exam Study Guide Chapter 1
FCS, Mr. Garcia
See page 67 to review 3-Dimensional figures.
1. A solid figure with all flat surfaces that enclose a single region of space is called a
p________________. Each flat surface or face is a polygon. The line segments where the faces intersect
are called e_________. The point where the 3 or more edges intersect is called a v________________.
2. A prism is a polyhedron with two parallel congruent f____________ called b____________ connected
by parallelogram faces. Draw one example.
3. A pyramid is a polyhedron that has a polygonal b______________ and 3 or more triangular
f_________ that meet at a common v_______________ (peak). Draw one example.
4. A cylinder is a solid with congruent parallel circular b____________ connected by a curved
s_____________. Draw a picture.
5. A cone is a solid with a circular base connected by a curved s________________ to a single
v____________. Draw a picture
6. A sphere is a set of points in space that are the same distance from a given p____________. A sphere
has no faces, no e________, and no v______________. Draw a picture.
7. Find the volume of a cube that has a total surface area of 54 square millimeters.
See page 69 for formulas of following 3-D figures:
8. Prism, regular pyramid, cylinder, cone, and sphere. Draw a picture of each figure listed and write the
formulas for volume and surface area underneath them.
9. Do problems on page 81-82: 32-43 (all).
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2013-14 Geometry
Semester 1 Final Exam Study Guide Chapter 1
FCS, Mr. Garcia
A word problem having to do with the equation of a line.
It’s the end of the semester, and the clubs at school are recording their profits. The Science Club started out at
$20 and has increased its balance by an average of $10 per week. The Math Club saved $5 a week and started
out with $50 at the beginning of the semester.
a)
Define x and y to fit the problem.
b)
make a table of values for each club.
c)
Write an equation for each club.
d)
Draw a complete graph for each rule and the same axes.
e)
When do the clubs have the same balance? Show how you can get this number both with the graph and
with the equations in c above.
f)
What is the balance at that point?
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2013-14 Geometry
Semester 1 Final Exam Study Guide Chapter 1
FCS, Mr. Garcia
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2013-14 Geometry
Semester 1 Final Exam Study Guide Chapter 1
FCS, Mr. Garcia
=============================================================================================
Chapter 2 Logic & Reasoning
Terms:
Deductive reasoning, inductive reasoning, conditional, hypothesis, conclusion, converse, contrapositive
Conditionals, Converse and Bi-Conditionals
A.
B.
C.
D.
E.
F.
G.
Restate each of the following given statement into an “if-then” statement.
Underline the hypothesis and circle the conclusion.
Is the statement true or false? Circle your answer.
Write the converse of the conditional and determine whether it is true or false.
Write the inverse of the conditional and determine whether it is true or false.
Write the contrapositive of the conditional and determine whether it is true or false.
If possible, write the bi-conditional statement in “if and only if” form. If not, write a counter example
demonstrating why not.
4.
Tardy students receive detention.
A. & B. ____________________________________________________________ C. T or F
D. ___________________________________________________________________T or F
E. ___________________________________________________________________T or F
F. ___________________________________________________________________T or F
G. ______________________________________________________________________
5.
All right angles are congruent.
A. & B. ____________________________________________________________ C. T or F
D. ___________________________________________________________________T or F
E. ___________________________________________________________________T or F
F. ___________________________________________________________________T or F
G. ____________________________________________________________________
1. A triangle is a polygon that has three sides.
A. & B. ____________________________________________________________ C. T or F
D. ___________________________________________________________________T or F
E. ___________________________________________________________________T or F
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2013-14 Geometry
Mr. Garcia
Semester 1 Final Exam Study Guide Chapter 1
FCS,
F. ___________________________________________________________________T
or F
G.
______________________________________________________________________
7.
Supplementary angles are two angles whose sum is 180.
A. & B. ____________________________________________________________ C.
T or F
D.
___________________________________________________________________T or F
E.
___________________________________________________________________T or F
F.
___________________________________________________________________T or F
G.
______________________________________________________________________
===============================================================
Chapter 3 Topics: parallel Lines & Their Relationships
===============================================================
Terms:
Parallel (//) lines, transversal, corresponding angles (=), alternate interior angles (=),
alternate exterior angles (=), same side (or consecutive) interior angles (sum of 180),
(supplementary angles still occur), parallel lines never intersect, parallel lines have the
same slope
===========================================================================
Refer to figure 4 to determine which lines if any are parallel.
1.
Given:
3. Given:
5. Given:
7. Given:
1  5 _____
2. Given: 8  12 _____
7  13 _____
4. Given: 4  14 _____
6  11 _____
6. Given: 10  15 _____
3 and 13 are supplementary _____
Given a b, l m . (Refer to figure 4)
b
a
3
16
13
5
7
4
1
2
6
14
l
15
11
12
9
8
8. If m 12 = 67 , then m 3 = ______
Figure 4
11
10
m
2013-14 Geometry
Mr. Garcia
Semester 1 Final Exam Study Guide Chapter 1
FCS,
9. If m 6 = 108 , then m 16 = ______
10. If m 4 = 123 , then m 10 = ______
11. If m 1 = 71 , then m 10 = ______
12. m1 = 2x + 7 and m16 = x + 30, x = _____, m1 = _____, m16 = _____
13. m11 = 3x + 6 and m13 = x + 26, x = _____, m11 = _____, m13 = _____
14. m2 = 11x - 16 and m7 = 7x + 28, x = _____, m2 = _____, m7 = _____
===============================================================
Chapter 4 Topics: Triangle Relationships
Term: {classified by angles} right (1 right  ), acute (all acute  ’s), obtuse(1 obtuse 
), equiangular triangles (all 60 angles). {Classified by sides}, Scalene (no sides are =),
isosceles (at least 2 sides are =), equilateral triangles (all sides are =) .sum of the interior
angles is 180°, sum of the remote interior angles is = to the exterior angle of the triangle,
==============================================================
Find the value of x.
1. x = _______
2. x = _______
3. x = _______
70
100
x
70
x
x
In ABC, find x and mA, then classify the type of triangle according to sides and
angels.
4. mA  6 x  24 , mB  2x  7 , and mC  x  4
x = ______, mA 
Classification:____________________
5. mA = 8x + 9, mB = 3x – 4, mC = 9x + 15
x = ______, mA 
Classification:____________________
Using the given information, classify each triangle according to its sides and angles.
12
2013-14 Geometry
Mr. Garcia
Semester 1 Final Exam Study Guide Chapter 1
FCS,

10. MNO , mM  27
6. DFZ , DF  DZ and m D = 90.

and mO  82 .
11. LJR ,
7. AWV , AW = AV and mA  90.
mL  35  and mR  104  .
8. PON , PO = 5, ON = 5, PN = 5.
12. KMN , mM 90, MN =
9. LJI , mL  45  and mI  90  .
13. SYX , mS = 60 and
MK.
mY = 60.
Use the distance formula to classify the triangle by the measure of its sides.
14. A(1, 0) B(3, 3) C(2, 4) AB = _____ BC = _____ AC = _____
Classification ________________
15. D(4, -6) A(-2, 5) V(0, 7) DA =_____ AV = _____ DV =
Classification: _______________
===============================================================
Chapter 4 Topic: Congruent Triangles
Term:
constructions of congruent triangles, 2 sides and the included angle are  (SAS), 2
angles and the included side are  (ASA), three congruent sides are  (SSS), 2 angles
and the non-included side are  (AAS),
2 sides and the non-included angle form 2 triangles (SSA).
===============================================================
Identify the congruent triangles and justify your answer. If congruency can not be proven
write “n p” in both blanks.
C
F
1.
Given: AB  ED, BC  EF , andCA  FD
A
BAC  __________ by _____________.
B D
E
M
2. Given: SM  MT , MP  MP, and MP bisects SMT
MPS __________ by _____________.
S
P
T
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2013-14 Geometry
Mr. Garcia
3. Given:
Semester 1 Final Exam Study Guide Chapter 1
OM  MN , PR  PQ, MO  PR,
and ON  RQ
MNO  _________ by ______________.
FCS,
O
M
Q
N
P
R
G
F
4. Given: FG  JK , GH  HK
H
HJK  _________ by _______________.
J
Given: C is the Midpoint of AD
ABC   _______by _________________
5.
K
A
B
C
E
D
6.
Given: XZ bisects YXW, YZX is a right angle.
XYZ   ________ by ________________
Y
For the following problems, ABC  DEF.
7.
Z
W
X
Given: AB = 3y + 12, DE = 5y – 18, find DE. ______
8. Given: mC = 4y – 23, m F = 2y – 5, find the mC. ______
9. Use the distance formula to determine whether the triangles with the given
vertices are congruent.
Given: ∆PQR : P(1,2), Q(3,6), R(6,5)
∆ KLM : K(-2,1), L(-6,3), M(-5,6)
PQ =
KL =
QR =
LM =
PR =
KM =
Are they Congruent?
Why?
Proofs:
14
2013-14 Geometry
Mr. Garcia
Semester 1 Final Exam Study Guide Chapter 1
1.
Given:
a b, l m
2.
Prove:
mÐ4 @ mÐ10
FCS,
m
1
n
2
5
b
Statements
14
15
16
1.
9
2
13
a
7
8
4
Reasons
6
10
11
2.
3.
2.
Given : AD //
BC ;
AD  BC
Prove: ∆ ABD  ∆ CDB
C
D
1
2
Statements
Reasons
3
4
B
A
1.
2.
3.
4.
5.
9. Use the graph to the right and use the
Pythagorean Theorem to determine the length of the longest segment.
Round to the nearest hundredth. Be sure to indicate the segment.
 A
D
List the segments order from least to greatest.
B
F
C
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2013-14 Geometry
Mr. Garcia
Semester 1 Final Exam Study Guide Chapter 1
FCS,
10. Use the graph to the right to answer the following questions. State the
coordinates for an endpoint of the segment with point B as one endpoint and point A
as a midpoint.
11. Given: C is the midpoint of BD , BC = (2x – 3)cm and CD = (5x – 24)cm.
Find the length of BD .
12. Find the value of x in the figure.
3x + 4
2x + 1
13. If mFBC = 74 and m 1 = 3x - 8 and m 2 = 5x + 26, find x and m 3.(4 points)
F
A
D
2
3
1
B
C
14. If m 1 = 41 , and m DOF = 87 , what is m 4?
15. If m 3 = 8x – 12 and m 4 = 4x + 6, and m 1 = 3x – 9,
find m 1 6.
16. If  3   4, then OD is a(n) ______________.
17. If GA // BF , their slopes are _______.

C
B
 D
2 3
A

1
E
4
O 6

5
F
G

Figure 2
18. If point B and point D are equidistant from AE , what conclusion
can be made about  1 and  4?
19. What is the sum of  1, 2, 3, 4, 5, and 6?
===============================================================
1
y  3   ( x  5)
3
If the equation of line 1 is
, state a possible equation which would
describe line 2.
16
2013-14 Geometry
Mr. Garcia
Semester 1 Final Exam Study Guide Chapter 1
FCS,
26. KNG is an isosceles triangle with K as the vertex angle, and KN  5x  2 , and
GK  2x  4 .
a. Draw a diagram and label the angles and the sides with their lengths in algebraic
form.
b. What is the length of KN ?
…Of KG ?
c. For what range of values for GN will the lengths still form a triangle ?
d. Make a table of lengths possible for NG . (Use only integers)
e. Using the range of values above, find 1 value that will form an ACUTE triangle.
Justify using the Pythagorean theorem.
f. Using the range of values above, find 1 value that will form an OBTUSE triangle.
Justify using the Pythagorean theorem.
==============================================================
27. In QRT, the angles listed from largest to smallest are:
a)  Q , R , T
b)  R , Q , T
c)  T , R , Q
d)  Q , T , R
Q
25
19
R
30
T
Why are the following triangles are congruent? Justify your reasoning! Be sure to use the
phrase “two sides and the included angle are congruent” instead of SAS!
32. Given : AB  CD ; AD  BC
33. Given: AE  BC ; E  C
Prove : ∆ABD  ∆ CDB
D is the midpoint of EC
Prove: ∆ADE  ∆BDC
34. Determine which postulate can be used to prove the triangles are congruent. If the
triangles cannot be proven congruent write NONE. Be sure to write out the postulate
(EX: 2 sides and the included angle are congruent instead of SAS)
C
D
A
A
B
B
E
C
D
17