Download Geometry Final Review

Name_____________________________________________Date_______________________Period________________
1st Semester Geometry Final Review
(1)
Write a vector describing the translation seen
on this set of axes?
(3) If x = 3, list the angles from smallest to largest.
(2)
Write a vector describing the following
translation:
(4) If x = 4 name the smallest angle.
(Picture not drawn to scale.)
A
3x - 2
2x - 3
x-2
x+3
C
B
15 -x
2x + 2
(5) What is the intersection of plane STXW and plane
SVUT?
a. SV
b. ST
c. YZ
d. TX
(6) What is the intersection of plane ABCD and plane
CDEF?
a. CD
b. AC
c. EC
d. EA
(7) If triangle ABC is reflected across the x- axis, what
would be the coordinate of B’?
(9) Classify the following triangle by its angles and its sides.
(Picture not drawn to scale.)
36°
6x – 20 + 2x + 36 = 180
6x + 20 = 2x + 36
6x -20 = 90
6x – 20 = 2x + 36
(10) Classify the following triangles by its angles and its
sides.
108°
(11) Given MO bisects angle < LMN.
m < LMO = 6x - 20, and m< NMO = 2x + 36.
Which of the following equations is used to find the
value of x?
a.
b.
c.
d.
(8) If the following image is reflected over x-axis, what are
the coordinates of the final image:
(12) Given BC bisects <ABD. Which equation can be used to
solve for the value of x?
a. 2X-10 = x+70
b. 2X-10 + x+70 = 180
c. 3x – 60
d. 2X-10 + X+70 = 90
(13) What would be the coordinates of A’B’C’ if the following
triangle were dilated by a scale factor of 2?
(14) Which of the following statements is true about the
dilation of the image?
(a) All corresponding angles increased by a scale
factor of 2
(b) All corresponding angles increased by a scale
factor of ½
(c) All corresponding sides increased by a scale factor
of 2
(d) All corresponding sides increased by a scale factor
of ½
(15) What type of segment is BD?
(16) Describe the following special segments:
a) Altitude – _______________________________
_______________________________________
_______________________________________
b) Median - ________________________________
________________________________________
________________________________________
c) Perpendicular Bisector-_____________________
________________________________________
________________________________________
(17) A plane takes off from a base at (8, 7) on a
coordinate grid. The pilot gets halfway to his
destination when he realizes he has to refuel. His
halfway point is at (7,5). What point is closest to his
destination
?
(18) A boy leaves his house at 4,5 on a coordinate
grid. When he gets halfway to school he realized he
forgot his homework. His halfway point is at (1, 3).
At which point is his school located?
a. (3, 6)
b. (3, 13)
c. (6, 3)
d. (6, 13)
a. (0,0)
b. (-2, 1)
c. (1, -2)
d. (7, 7)
(19) Describe this transformation:
(20) Which of the following statements would describe the
transformation shown in the picture:
(a)
(b)
(c)
(d)
A 45° rotation about the origin
A 90° rotation about the origin
A reflection across y = -1/2x
A translation
(21) Find the value of angle R If angle S = 72°
(22) Write an equation to find the value of X if
S  (3x  4)° and U  (3x  4)° and T  ( x  2)°
(23) A geometry student concluded that:
(24) Draw a counterexample for the following conclusion:
If 2 sides and a non-included angle of one triangle are
congruent to 2 sides and a non-included angle of another
triangle, then the triangles are congruent.
If all of the angles in one triangle are congruent to all of the
angles in another triangle, then the triangles are
congruent.
Which diagram could be used as a counterexample to his
conclusion?
A.
C.
B.
D
(25) AF bisects  CAB. If  CAB= 78˚,
 FAB = 5x + 3 and find x.
(26) In the diagram below, YT bisects WYZ . If the
m3  108 and m  2 = 2x + 4 then what is the m2
and m1?
W
3
X
Y
T
2
1
Z
(27) Find the value of x.
(28) Find the value of x.
(29) Rico’s home is at coordinates (-2, 4). He decides to
meet his friend Paul at a coffee shop that is at
coordinates (5, 8). The coffee shop is at the midpoint
between Rico’s and Paul’s homes. What are the
coordinates of Paul’s home?
(30) What is the midpoint of (4,4) and (-2, -7)?
(31) Which of the following could not be the 3rd side if 2
side lengths of the triangle were 3 and 10?
A. 11
B. 7.2
C. 6
D. 12.3
(32) Which of the following could not be the 3rd side if 2
side lengths of the triangle were 18 and 12?
A. 11.3
B. 6.2
C. 29.9
D. 5.4
(33) Determine the intersection of the 2 planes:
(34) Find the intersection of planes D and H
D
D
(35) Which congruency postulate proves the triangles
congruent?
A.
B.
C.
D.
E.
SSS
SAS
AAS
ASA
Not Congruent
(37) Which congruency postulate proves the triangles
congruent?
A. SSS
B. SAS
C. AAS
D. ASA
E. Not Congruent
(39) Which statement must be true if you want to use the
given shortcut to prove the triangles congruent?
A.
B.
C.
D.
<D = <A
<B = <C
AB = CD
AM = DM
(36) Which congruency postulate proves the triangles
congruent?
A. SSS
B. SAS
C. AAS
D. ASA
E. Not Congruent
(38) Which congruency postulate proves the triangles
congruent?
A.
B.
C.
D.
E.
SSS
SAS
AAS
ASA
Not Congruent
(40) Which statement must be true if you want to use the
given shortcut to prove the triangles congruent?
A.
B.
C.
D.
<Z = <W
<ZYX = <WYX
XZ = XW
WY = ZY
(41) Fill in the reasons for the following proof.
Given: M is the midpoint of BY
AM = MZ
Prove: ∆ABM = ∆ZYM
Statements
M is the midpoint of
BY
BM = YM
<B = <Y
AB = XY
∆ABM = ∆XYM
Reasons
Given
Definition of midpoint
Definition of ________
_____________
Given
________ congruency
postulate
(42) Fill in the reasons for the following proof.
Given: <B = <D
C is the midpoint of BD
Prove: ∆ABC = ∆EDC
Statements
C is the midpoint of BD
BM = YM
<ACB = <ECD
<B=<D
∆ABM = ∆XYM
(43) Solve for X.
(44) Solve for X.
(45) Find X.
(46) Find X.
Reasons
Given
Definition of midpoint
Definition of ________
_____________
Given
________ congruency
postulate