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Geometry 1st Semester Review 2011
FCS, 2011-12, Mr. Garcia
Name_________________________________
Date___________________
Period______
This is your semester exam which is worth 10% of your semester grade. You can determine grade “what-ifs” by
using the equation below.
(Current Re nWeb Grade)x.90 + (semester exam grade) 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
Terms:
y2 - y1
, space, collinear, noncollinear, coplanar, noncoplanar,
x2 - x1
x  x y  y2
sum of x ' s sum of y ' s
,
) or ( 1 2 , 1
) , congruent
a2  b2 or (x2 - x1 )2 + ( y2 - y1 )2 , midpoint (
2
2
2
2
Point, line, plane, segment, ray, angle, angles, vertex, slope of a line
distance
segments (are =in length), Segment addition propery.
Chapter 1 Topics: refer to the figure to the right to answer problems 1 - 15.
X
______1. The line intersecting plane P.
______2. The intersection of AC and XF .
A
______3. Are points B, F, and X collinear?
______4. Are points A, B, and X coplanar?
B
D
______5. Are points A, B, and X contained in Plane P?
C
F
P
____ ____ ____6. Identify 3 non-collinear points
____ ____ ____ ____7. Identify 4 non-coplanar points.
j
______, ______ 8. Identify 2 angles that have B as their vertex.
______9. Name a line.
______10. Name a ray.
12. If B is the midpoint of AC and AB = 2x – 3 and BC = 5x – 24, find x, AB, and BC.
_____, _____, _____
13. If XB = 14 and XF = 20, find BF. ______
14. If B is the midpoint of XF and XB = x + 11 and BF = 5x – 1, find x and XF. ____, ____
15. If AB = 3x, BC = x + 2, and AC = 38, find x and AB. _____, _____
1
Geometry 1st Semester Review 2011
FCS, 2011-12, Mr. Garcia
16. If the coordinate of G is –8 and the coordinate of H is 9, find GH. ______
17. 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)_____
18. 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. _____
19. How many sides does a pentagon have? ______
20. What does it mean for a polygon to regular? ____________________
21. Find the perimeter of a regular hexagon with a side equal to 5. ______
Chapter 2 Topics: Logic & Reasoning
Terms:
Deductive reasoning, inductive reasoning, conjecture, conditional, hypothesis, conclusion, converse,
contrapositive, counterexample
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. ______________________________________________________________________
6.
A triangle is a polygon that has three sides.
A. & B. ____________________________________________________________ C. T or F
D. ___________________________________________________________________T or F
E. ___________________________________________________________________T or F
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. ______________________________________________________________________
A.
B.
C.
D.
E.
F.
G.
2
Geometry 1st Semester Review 2011
FCS, 2011-12, Mr. Garcia
Chapter 3 Topics: Angle Relationships
Terms:
angle, sides of an angle, naming an angle ( BDG means point D is the vertex of the angle), right (= 90º),
acute (< 90º ) and obtuse angles (>90º ), congruent angles(  ) adjacent angles, vertical angles, complementary
angles(sum is 90º), supplementary angles (sum is 180º), linear pair(sum is 180º), perpendicular lines (Lines that
2
3
form 90º angles), slope of perpendicular lines are “opposite reciprocals” ( If m  , then m   )
3
2
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

E

5
6
F

G
Figure 2
Refer to figure 2 to solve problems 1 - 5.
10. If m3 = 27, then m4 = _____
11. 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 = _____.
14. If OD  BF , then m4 + m5 = _____.
15. If OD  BF and m4 = 65, then m1 = _____,
m2 = _____, m6 = _____, mAOF = _____.

C 
D
B
3
2
A

4
1
O

6
5
F

G
16. If OD  BF , name all the pairs of complementary angles.______________
_____________________________________________________________
17. If OD is the  bisector of BF , which segments are congruent? __________
E

Figure 2
Refer to figure 3 to solve problems 18 - 22.
18.
19.
20.
21.
Given:
Given:
Given:
Given:
m2 = 9x +28 and m3 = 47 – 2x, x = _____, m2 = _____
m1 = 3x + 5 and m3 = 65, x = _____
m2 = 9x +2 and m4 = 7x + 36, x = _____, m2 = _____
m1 = x-9 and m2 = 2x, x = _____, m1 = _____
2
1
3
4
Figure 3
3
Geometry 1st Semester Review 2011
FCS, 2011-12, Mr. Garcia
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.
3.
5.
7.
Given:
Given:
Given:
Given:
Given
1  5 _____
7  13 _____
6  11 _____
3 and 13 are supplementary
a b, l m .
2. Given: 8  12 _____
4. Given: 4  14 _____
6. Given: 10  15 _____
_____
b
a
3
16
13
5
7
4
1
2
(Refer to figure 4)
8. If m 12 = 67o , then m 3 = ______
9. If m 6 = 108o, then m 16 = ______
10. If m 4 = 123o, then m 10 = ______
11. If m 1 = 71o, 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 = _____
6
14
l
15
11
12
9
8
m
10
Figure 4
Find the slope of the line through the given points.
15. a. A(-3,8), B(4,2) _____
b. What is the slope of any line parallel to the line through points A and B? _____
c. What is the slope of any line perpendicular to the line through points A and B? _____
16. a. C(1,-3), D(9,-9) _____
b. What is the slope of any line parallel to the line through points C and D? _____
c. What is the slope of any line perpendicular to the line through points C and D? _____
17. a. E(-2,-3), F(-6,-5) _____
b. What is the slope of any line parallel to the line through points E and F? _____
c. What is the slope of any line perpendicular to the line through points E and F? _____
Chapter 4 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
x
70
x
4
Geometry 1st Semester Review 2011
FCS, 2011-12, Mr. Garcia
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  2 x  7 , and mC  x  4
x = ______, mA 
Classification:_by sides:___________________ by angles: ____________________
5. mA = 8x + 9, mB = 3x – 4, mC = 9x + 15
x = ______, mA 
Classification:_by sides:___________________ by angles: ____________________
Using the given information, classify each triangle according to its sides and angles.
6. DFZ , DF  DZ and m D = 90.
10. MNO , mM  27  and mO  82  .
11. LJR , mL  35  and mR  104  .
7. AWV , AW = AV and mA  90.
8. PON , PO = 5, ON = 5, PN = 5.
12. KMN , mM 90, MN = MK.
9. LJI , mL  45  and mI  90  .
13. SYX , mS = 60 and 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). See page 215 for
right triangle congruence.
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 , and CA  FD
BAC  __________ by _____________.
A
B D
M
2. Given: SM  MT , MP  MP, and MP bisects SMT
MPS __________ by _____________.
S
T
P
3. Given: OM  MN , PR  PQ, MO  PR, and ON  RQ
MNO  _________ by ______________.
4. Given: FG  JK , GH  HK
HJK  _________ by _______________.
5.
6.
Given: C is the Midpoint of AD
ABC   _______by _________________
Given: XZ bisects YXW, YZX is a right angle.
XYZ   ________ by ________________
F
E
O
M
Q
N
G
P
R
H
J
A
K B
C
D
E Y
Z
W
5
X
Geometry 1st Semester Review 2011
FCS, 2011-12, Mr. Garcia
For the following problems, ABC  DEF.
7. 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)
4
PQ =
∆ KLM : K(-2,1), L(-6,3), M(-5,6)
KL =
QR =
LM =
PR =
KM =
Are they Congruent?
Why?
Proofs:
1. Given : a // b and m // n
Prove:  4   10
Statements
m
1 2
4 3
Reasons
b
5
n
6
8 7
1.
14
2.
a
3.
15
16
10
9
12
11
4.
2.
Given : AD //
BC ; AD  BC
Prove: ∆ ABD  ∆ CDB
Statements
Reasons
C
D
1
1.
2.
2
3
4
A
B
3.
4.
6
Geometry 1st Semester Review 2011
1. Describe the location of point E.
FCS, 2011-12, Mr. Garcia
Point A. Point D.
E
2. Where does to triangle formed by points B, E, and C lie?
3. Where does the line containing points B and C lie?
C
B
M
D
A
4. Does a line containing point E have to intersect the plane?
I
•
G
H
5. If GHK is a right triangle, name another right triangle.
•
J
K
L •
O
M
7. Name a pair of alternate interior angles.
F
8. Name a pair of corresponding angles.
•
P
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.
 A
Be sure to indicate the segment. List the segments in
D
order from least to greatest.
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.
B
F
C
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
7
Geometry 1st Semester Review 2011
FCS, 2011-12, Mr. Garcia
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.
16. If  3   4, then OD is a(n) ______________.
17. If GA // BF , their slopes are _______.
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?
C
B

 D
2 3
A

1
O
E
4

5
6
F
G

Figure 2
1
If the equation of line 1 is y  3   ( x  5) , state a possible equation which would describe line 2.
3
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
B
8
E
A
B
D
C
Geometry 1st Semester Review 2011
FCS, 2011-12, Mr. Garcia
9