10R Geometry Mid Term Review # 1
PART I:
Name: ___________________________
Answer all questions in this part. Each correct answer will receive 2 credits.
No partial credit will be allowed. Record your answers on the line provided.
Use this space for computations.
1. Write the inverse of the statement
“If I do not study for the midterm exam, then I will regret my exam grade.”
1.
2.
3.
4.
If I do not study for the midterm exam, then I will not regret my exam grade.
If I regret my exam grade, then I did not study for the midterm exam.
If I do not regret my exam grade, then I did study for the midterm exam.
If I study for the midterm exam, then I will not regret my exam grade.
2. The statement “Julie plays the flute or Julie is a member of math club” is false.
Which statement is true?
1.
2.
3.
4.
Julie plays the flute and Julie is a member of math club.
Julie plays the flute and Julie does not join the ski club.
Julie does not play the flute and Julie is a member of math club.
Julie does not play the flute and Julie is not a member of math club.
3. A teacher is sent to monitor three rowdy groups of students that are sitting in three different locations
in the Taft cafeteria. Where should the teacher stand so that they have an equal ground to cover if
they have to get to one of the groups of students quickly?
1. circumcenter
2. incenter
3. centroid
4. orthocenter
A
4. In the figure shown to the right, BC DE , AB  9 yards,
BC  12 yards, AE  20 yards, and DE  16 yards. Find CE.
1. 8
2. 12
3.
4.
B
15
5
C
D
E
Figure is not drawn to scale.
1.
2.
a b
a b
3.
4.
112 m2
504 m2
3.
4.
70
ab
we cannot determine their relationship
6. The base of a triangle is 6 meters and its area is 84 m2. The base of a
similar triangle is 18 meters. What is the area of the larger triangle?
1.
2.
a
756 m2
252 m2
b
4y +14 °
°
Revised: 3/22/2016 2:16 AM
5. If y = 23, what do we know about line a and b?
1
7. Find the value of x.
50
1. 85
2. 60
3.
4.
95
65
65
x
70
Figure is not drawn to scale.
8. In the accompanying diagram of quadrilateral RSTU,
RSW is isosceles, W is the midpoint of UT ,
RU  UW and ST  WT . RWU can be proven 
to SWT by
1. SAS  SAS
2. SSA  SSA
PART II:
3. HL  HL
4. AAS  AAS
R
U
S
W
T
Answer all questions in this part. Each correct answer will receive two (2) credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. For all questions in this part, a correct numerical answer with no work shown will
receive only one (1) credit.
10.
Point M is between S and T on ST . If SM  x 2  8 x , MT  18  2x , and ST  90 inches, find the
value(s) of x.
11.
Given that mDAC  5 y , mABC  2 y  4 , and mACB  6 y  58 , find the value of y.
D
A
B
C
Revised: 3/22/2016 2:16 AM
9.
2
PART III:
On the set of axes below, graph and label ABC with vertices at A(-8, -8), B(-4, 4), and C(8, -4).
DE is the midsegment of ABC . D is on BC and E is on AC . Graph DE .
Show DE 
1
AB
2
13. What is the equation of the perpendicular bisector
of HI , whose coordinates are H(1, 5) and I(9, 1).
Use of the graph is optional.
Revised: 3/22/2016 2:16 AM
12.
Answer all questions in this part. Each correct answer will receive four (4) credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. For all questions on this part, a correct numerical answer with no work shown will
receive only one (1) credit.
3
14.
Answer all questions in this part. Each correct answer will receive six (6) credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. For all questions in this part, a correct numerical answer with no work shown will
receive only one (1) credit.
Given:
AD is an altitude of ABC
AD bisects BAC
F is a right 
AC bisects DF
E  DAB
Prove:
DAC  FEC
A
B
E
D
C
F
Revised: 3/22/2016 2:16 AM
PART IV:
4
10R Geometry Mid Term Review # 2
PART I:
In the accompanying diagram, WX || ZY WZ || XY . By which
method can ΔWZY be proven congruent to ΔYXW?
(1)
(2)
(3)
(4)
2.
If I don't go swimming, then it is Thursday.
If it is not Thursday, then I will not go swimming.
If I go swimming, then it is Thursday.
If I don't go swimming, then it is not Thursday.
4
22
11
8
Given right ΔABC, with mB  34 , if DC is an angle bisector,
find mADC .
(1)
(2)
(3)
(4)
5.
SAS  SAS
ASA  ASA
AAS  AAS
HL  HL
In XYZ , AD  BD  CD . If mAXC  4x  6 , mAXD  x  7 ,
what is mDXC ?
(1)
(2)
(3)
(4)
4.
Use this space for computations.
Which of the following is the contrapositive of the statement,
"If it is Thursday, I will go swimming."
(1)
(2)
(3)
(4)
3.
Answer all questions in this part. Each correct answer will receive 2 credits. No partial credit
will be allowed. Record your answers on the line provided.
56°
62°
28°
46°
Given segment ABCD, which of the following is not always true?
(1)
(2)
(3)
(4)
AB + BC + CD = AD
AC - AB = BC
AB = CD
AD > AB + BC
Revised: 3/22/2016 2:16 AM
1.
Name: ___________________________
5
In ΔABC, if AS = CS, AP = 16, BP = x + 5, and PT = 2x - 4,
then P is a/an________ and x = _______:
(1)
(2)
(3)
(4)
PART II:
Circumcenter, 11
Centroid, 6
Incenter, 6
Centroid, 8
Answer all questions in this part. Each correct answer will receive two (2) credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. For all questions in this part, a correct numerical answer with no work shown will
receive only one (1) credit.
7.
Given ΔABC, with A(-1, -1), B(2, 3), and C(4, -3). Find the length and slope of midsegment DE ,
where D is on AB , and E is on AC .
8.
Write the equation of the line perpendicular to the line 3 y  x  6 through the point (6, -1).
PART III:
9.
Answer all questions in this part. Each correct answer will receive four (4) credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. For all questions on this part, a correct numerical answer with no work shown will
receive only one (1) credit.
In XYZ below, A and D are points on XY , and B and C are points on XZ such that AB || DC || YZ .
Find CZ .
2y
Revised: 3/22/2016 2:16 AM
6.
6
10.
Answer all questions in this part. Each correct answer will receive six (6) credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. For all questions in this part, a correct numerical answer with no work shown will
receive only one (1) credit.
Given:
DE and BF are altitudes,
AE  CF , and DE  BF
Prove:
AB || CD
Revised: 3/22/2016 2:16 AM
PART IV:
7
10R Geometry Mid Term Review # 3
PART I:
Name: ___________________________
Answer all questions in this part. Each correct answer will receive 2 credits. No partial credit
will be allowed. Record your answers on the line provided.
1. Determine which of the following pairs of lines are not parallel to each other.
a. y = -3x + 9
2y = -6x – 8
b. 4x – 2y = -10
7y – 14x = 12
3
x+2
5
-3x + 5y = 9
c. y =
d. –y = 5x + 3
2y = 10x – 8
2. Write the logically equivalent statement to “If it is sunny, then we will go swimming.”?
a.
b.
c.
d.
3.
If it is not sunny, then we will not go swimming.
If it is sunny, then we will go swimming.
If we don’t go swimming, then it is not sunny out.
If we go swimming, then it is sunny out.
 1 and  2 form a linear pair.  1 is 24 more than twice  2. What is the value of  1?
a. 52
c. 104
b. 68
d. 128
4. The perimeter of a triangle ABC is equal to 72 inches. If the sides of a triangle are AB = x + 16,
BC = 5x – 20, and AC = 2x + 12, list the angles in order from smallest to largest.
a. B, C, A
c. C , B, A
b. A, C, B
d. A, B, C
a.
c.
circumcenter
orthocenter
b. incenter
d. centroid
6. A line segment joining the vertex of a triangle to the midpoint of the side opposite is called:
a. an altitude
c. an angle bisector
b. a median
d. a perpendicular bisector
Revised: 3/22/2016 2:16 AM
5. Three medians of a triangle intersect at a
8
7. The vertices of ABC are A( 1,2), B( 1,2) and C(6,0). Which conclusion can be made about the
angles of ABC ?
a. mA  mB
c. mA  mC
b. mACB  90
d. mABC  60
8. Which statements could be used to prove that ABC and AB C  are congruent?
a.
AB  AB , BC  B C ,and A  A
b. AB  AB , A  A,and C  C 
c. A  A, B  B , and C  C
d. A  A, AC  AC ,and BC  B C 
PART II:
Answer all questions in this part. Each correct answer will receive two (2) credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. For all questions in this part, a correct numerical answer with no work shown will
receive only one (1) credit.
9. Write a two-column proof of the following:
Given: BC  DE
Prove: BD  CE
What is the measure of the acute angle formed by Jay Street and Main Street?
Revised: 3/22/2016 2:16 AM
10. The accompanying diagram shows two parallel streets, Main Street and Brooks Road, intersected by
Jay Street. The obtuse angle that Jay Street forms with Brooks Road is three times the measure of the
acute angle that Jay Street forms with Main Street.
9
PART III:
Answer all questions in this part. Each correct answer will receive four (4) credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. For all questions on this part, a correct numerical answer with no work shown will
receive only one (1) credit.
11. AB and CD intersect at point E, mAEC  6 x  20 , and mDEB  10 x . What is the mCEB ?
PART IV:
Answer all questions in this part. Each correct answer will receive six (6) credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. For all questions in this part, a correct numerical answer with no work shown will
receive only one (1) credit.
C
12. Given: AC  DC and BA  ED .
Prove: ACE  DCB
E
B
D
Revised: 3/22/2016 2:16 AM
A
1
0
10R Geometry Mid Term Review # 4
PART I:
Which equation represents a line that is parallel to the line y  4 x  5?
(1)
(3)
2.
(4)
y  4x  5
Figure 1, only
Both Figure 1 and Figure 2
(2)
(4)
Figure 2, only
Neither Figure 1 nor Figure 2
2 2
(2)
4 3
(3)
10
(4)
5 2
50 miles
(2)
350 miles
(3)
550 miles
(4)
650 miles
What is the value of y in the figure below?
(1)
(3)
6.
2 y   x  20
The direct distance between city A and city B is 200 miles. The direct distance
between city B and city C is 300 miles. Which could be the direct distance
between city C and city A?
(1)
5.
(2)
The coordinates of point R are (–3,2) and the coordinates of point T are (4,1).
What is the length of RT ?
(1)
4.
2 y  8 x  6
1
y  x3
4
Use this space for computations.
In which of the accompanying figures are segments XY and YZ perpendicular?
(1)
(3)
3.
Answer all questions in this part. Each correct answer will receive 2 credits. No partial credit
will be allowed. Record your answers on the line provided.
21
80
(2)
(4)
16
29
80
4y +16 °
°
The base of an isosceles triangle is 5 and its perimeter is 11. The base of a
similar isosceles triangle is 10. What is the perimeter of the larger triangle?
(1)
(3)
15
22
(2)
(4)
21
110
Revised: 3/22/2016 2:16 AM
1.
Name: ___________________________
1
1
7.
The measures of two complementary angles are represented by (3x  15)
and (2 x  10). What is the value of x?
(1)
8.
17
(2)
19
(3)
35
(4)
37
In DEF , an exterior angle at F is represented by 8x + 15. If the two non-adjacent
interior angles are represented by 4x + 5 and 3x + 20, find the value of x.
F
(1)
(2)
(3)
(4)
PART II:
9.
2.5
9
10
15
D
8x+15
4x+5 3x+20
E
Answer all questions in this part. Each correct answer will receive two (2) credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. For all questions in this part, a correct numerical answer with no work shown will
receive only one (1) credit.
Write a statement that is logically equivalent to the statement “If two sides of a triangle are
congruent, the angles opposite those sides are congruent.”
________________________________________________________________________________
10.
Plane Q intersects two parallel planes, plane P and plane R. Describe the intersection of Plane Q with
parallel planes P and R. Draw a sketch to support your answer
11.
1 and 2 form a linear pair. If the measure of 1 is five more than four times the measure of 2 ,
find the measure of 2 .
12.
Write the equation for the line shown in the accompanying
graph. Explain your answer.
Revised: 3/22/2016 2:16 AM
Identify the new statement as the converse, inverse, or contrapositive of the original statement.
__________________
1
2
PART III:
13.
Answer all questions in this part. Each correct answer will receive four (4) credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. For all questions on this part, a correct numerical answer with no work shown will
receive only one (1) credit.
On the set of axes below, graph and label ABC with vertices at A(-8, -8), B(-4,4), and C(8,-4).
If D is the midpoint of BC and E is the midpoint of AC , state the coordinates of D and E and label
each point on your graph.
Explain why DE AB .
AB and CD intersect at point E, mAEC  x  y , mAED  x , and mBEC  y  30 .
Find the value of x and y. Only an algebraic solution will be accepted for full credit.
Revised: 3/22/2016 2:16 AM
14.
1
3
15.
Given:
Prove:
Answer all questions in this part. Each correct answer will receive six (6) credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. For all questions in this part, a correct numerical answer with no work shown will
receive only one (1) credit.
G
Isosceles GIF with vertex I
IH is the median to GF
GIH  FIH
I
H
F
Revised: 3/22/2016 2:16 AM
PART IV:
1
4
10R Geometry Mid Term Review # 5
Name:_____________________________
PART I:
Answer all questions in this part. Each correct answer will receive 2 credits. No partial credit
will be allowed. Record your answers on the line provided.
1._____
In the accompanying diagram, WX  ZY, WX  WZ, and ZY  WZ .
By which method can WXZ  ∆ZYW?
1.
2.
Which of the following is the converse of the statement:
"If it is Thursday, I will go swimming."
1.
2.
3.
4.
3.______
40
120
140
20
Which of the following forms a plane, by definition?
1.
2.
3.
4.
6. ______
x = 12
x=3
x=4
x=9
Given isosceles ∆ABC, with the measure of vertex  B = 100.
The bisectors of A and C are drawn, they intersect at point D.
What is the measure of ADC?
1.
2.
3.
4.
5. ______
If I don't go swimming, then it is not Thursday."
If it is not Thursday, then I will not go swimming.
If I go swimming, then it is Thursday.
If I go swimming, then it is not Thursday.
In XYZ, AD = 4x, CZ = 9, DZ = 15. If D is an incenter, what is the value of x?
1.
2.
3.
4.
4. _____
3. AAS  AAS
4. HL(Rt)  HL(Rt)
three points
two intersecting lines
two perpendicular lines
four points
In ∆ABC, if AX = BX = CX, then X is an:
1.
2.
3.
4.
Orthocenter
Centroid
Circumcenter
Incenter
Revised: 3/22/2016 2:16 AM
2. _____
SAS  SAS
ASA  ASA
1
5
PART II:
Answer all questions in this part. Each correct answer will receive two (2) credits.
Clearly indicate the necessary steps, including appropriate formula substitutions,
diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer
with no work shown will receive only one (1) credit.
7. Given ∆XYZ, A, B, and C are midpoints of the sides,
BC = 4x - 1, and YZ = 5x + 4. Find the length of YA.
8.
Given ∆ABC, with A(7, 2), B(0, 6), and C(-1,0).
Find the length of median BD, the median from
B to side AC.
Given: “A triangle has three sides or a square has five sides.”
Determine the truth value of the disjunction and justify your answer.
Revised: 3/22/2016 2:16 AM
9.
1
6
PART III:
In  XYZ to the right, A is a point on XY, and B is a point on XZ such that AB || YZ .
If XA = x + 1, AB = 6, AY = x – 5, and YZ = x, find the length of AX.
PART IV:
11.
Answer all questions in this part. Each correct answer will receive six (6) credits.
Clearly indicate the necessary steps, including appropriate formula substitutions,
diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer
with no work shown will receive only one (1) credit.
Graph and label quadrilateral ABCD. With A (-3, 2), B(6, 6), C(3, 9) and D (-6, 5).
a.)
Find the midpoint of side CB.
b.)
Show the length of AD equals the length of BC.
Express lengths in simplest radical form.
c.)
Prove that AB || DC.
Revised: 3/22/2016 2:16 AM
10.
Answer all questions in this part. Each correct answer will receive four (4) credits.
Clearly indicate the necessary steps, including appropriate formula substitutions,
diagrams, graphs, charts, etc. For all questions on this part, a correct numerical answer
with no work shown will receive only one (1) credit.
1
7
10R Geometry Mid Term Review # 6
Name:_____________________________
PART I:
Answer all questions in this part. Each correct answer will receive 2 credits. No partial credit
will be allowed. Record your answers on the Scantron provided.
______ 1. What is the equation of a line that is parallel to 2y + 4x = 2
and passes through (1,4)?
1) y = -2x + 1
3) y = ½ x + 1
Use this space for
computations
2) y = ½ x + 6
4) y = -2x + 6
______2. The medians of ABC are AD, BE, and CF, and the centroid is P. If AP = 8, find
the length of AD.
1) 8
3) 12
2) 4
4) 16
_______3. In three-dimensional space, two planes are parallel and a third plane intersects both of the parallel
planes. The intersection of the planes is a
______4.
1) plane
2) pair of parallel lines
3) point
4) pair of intersecting lines
For which of the following are the marked sides and angles not sufficient to prove
that the triangles are congruent?
1) 2, 2, 3
3) 3, 3, 5
2) 2, 3, 4
4) 3, 3, 6
______6. Given that AB CD and EFGH is a transversal, determine the
measure of AFE, if mAFG = 8x and mFGC = 6x – 30.
1) 15
3) 120
2) 60
4) 90
Revised: 3/22/2016 2:16 AM
______5. Which of the following can not be the measure of the sides of a triangle?
1
8
B
______7. In ABC, BP  AC, ABN  CBN , and AM  CM .
Segment BN represents a(n)
1) angle bisector
2) perpendicular bisector
3) median
4) altitude
A
M
N P
C
______8. In the figure below, if you are given that CE  AB and AD  BC ,
and you are asked to prove ADB  CEB indirectly, what must
your assumption be?
1) ADB  CEB
3) CE is not  AB
Answer all questions in this part. Each correct answer will receive two (2) credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. For all questions in this part, a correct numerical answer with no work shown will
receive only one (1) credit.
9.
In PQR, S is the midpoint of RQ and T is the midpoint of PQ . RP = 8x –2, ST = 3x + 6,
SR = 7x – 3, and PQ = 10x +2. Find ST, RP, SR, RQ, PQ, and TQ.
10.
Find the coordinates of the centroid of ABC with vertices A(-2, 2), B(6, 2), and C(2, 14).
Revised: 3/22/2016 2:16 AM
PART II:
2) ADB is not  CEB
4) AD is not  BC
1
9
11. Complete the following:
a) Write the converse, inverse and contrapositive of the statement below in words.
b) Give the truth value of the conditional (the original statement).
c) Give the truth value of the contrapositive.
If Rochester is a city, then Rochester is the capital of New York.
a.)
Converse:
__________________________________________________________________
b.)
Inverse:
__________________________________________________________________
c.)
Contrapositive:__________________________________________________________________
12.
The intersection of PQ and RS is T. If m PTR = x, mQTS = y, and mRTQ =2x + 45, find the
measure of PTR, QTS, RTQ, and PTS.
PART III:
Answer all questions in this part. Each correct answer will receive four (4) credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. For all questions on this part, a correct numerical answer with no work shown will
receive only one (1) credit.
Given:
Prove:
13. Complete the following proof: If DR bisects CDA, 3 ≅1, and 4 ≅2, then 3 ≅ 4.
Reason
Revised: 3/22/2016 2:16 AM
Statement
2
0
14. Fill in the blanks on the following proof
.
Statement
1. S is a midpoint on
PQ
Reason
1. Given
RS is an altitude
2. PS  QS
Given:
S is a midpoint on PQ
3.
3. Altitudes   Seg
4. PSR & QSR
are rt. 
5. PSR  QSR
4.
RS is an altitude
Prove:
PQR is isosceles
6.
7. PSR  QSR
8. PR  QR
9. PQR is isosceles
PART IV:
2.
5.
6. Reflexive Property
7. SAS  SAS
8.
9. 2  sides → isosceles Δ
Answer all questions in this part. Each correct answer will receive six (6) credits. Clearly
indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,
charts, etc. For all questions in this part, a correct numerical answer with no work shown will
receive only one (1) credit.
15. The coordinates of the vertices of ABC are A(-1, 0), B(5, 0), and C(2, 4)
a. If CD is the altitude to AB, what are the coordinates of D?
b. What is the length of AB?
d. What is the area of ABC?
e. What is the orthocenter of ABC?
Revised: 3/22/2016 2:16 AM
c. What is the length of CD?
2
1