Honors Geometry
First Semester Final Exam Review
Part I: Proofs
1. Given: AB  BC
AE  EC
Prove: AD  DC
Name: _____________________
3.
4.
Prove:
ABDE is a parallelogram
BC is the base of isosceles ΔBCD
ACDE is an isosceles trapezoid
Given:
Prove:
Given: TVAX is a rectangle
TXV  VAT
6.
5.
Given:
2.
Given:
Prove:
Given:
Prove:
Given:
Prove:
7.
Given:
Prove:
9.
Given:
Prove:
FJ is the base of an isosceles ∆
FG  JH, O is the midpoint of MF
K is the midpoint of MJ
OH  KG
A  D
C bisects BE
AB  ED
8.
Given:
Prove:
OH is altitude to GJ
OH is median to GJ
G  J
RSOT is a parallelogram
MS  TP
MOPR is a parallelogram
AD  BC
DAB  CBA
ΔABE is isosceles
BA  AC
DC  AC
DC  BA
B  D
1  2
3  4
Prove: ΔABE  ΔDCE
10. Given:
Part II: Final Exam Review. You may need to draw the diagram to solve the problem.
1
1. Find x.
2. Answer always, sometimes, or never.
a) If a triangle is obtuse it is isosceles.
b) The bisector of the vertex angle of a scalene ∆ is perpendicular to the base.
c) If one of the diagonals of a quadrilateral is the perpendicular bisector of the
other the quadrilateral is a kite.
d) Supplements of complementary angles are congruent.
3. FGHJ is a parallelogram, FG = x + 5, GH = 2x + 3, mG = 40°, mJ = 4x + 12. Find: mF, perimeter of FGHJ
4. ABCD is a parallelogram, mA = 3x + y, mD = 5x + 10, mC = 5y + 20. Find mB.
5. The measure of the supplement of an angle exceeds three times the measure of the complement of the angle
by 12°. Find the measure of half of the supplement.
6. Write the most descriptive name for each figure:
a) A four-sided figure in which the diagonals are perpendicular bisectors of each other.
b) A four-sided figure in which the diagonals bisect each other.
c) A triangle in which there is a hypotenuse.
d) A four-sided figure in which the diagonals are  and all sides are  .
7. If one of two supplementary angles is 16° less than three times the other find the measure of the larger.
8. Two consecutive angles of a parallelogram are in the ratio of 7 to 5. Find the measure of the larger.
9. Find m1 if a ║ b.
11. a) How many points determine a line?
c) Collinear means?
10. Given: ΔFJH is isosceles with base JH,
K and G are midpoints, FK = 2x + 3,
GH = 5x – 9, JH = 4x
Find: The perimeter of ΔFHJ
b) How many non-collinear points determine a plane?
d) Coplanar means?
2
12. Fill in each blank with line, segment, or ray.
a) A _____________________ has one endpoint. b) A _____________________ has a definite length.
c) A _____________________ can be bisected. d) A _____________________ has two endpoints.
e) A _____________________ has no endpoints. f) A _____________________ has no midpoints.
g) The union of two opposite rays is called a _____________________.
13. SR = RQ = QT and T is the midpoint of SM.
a) If SR = 20, then RT = _______
b) If TM = 45, then RQ = _______
c) If QT = 12, then QM = _______
d) If RT = 8, then SM = _______
14. Use the figure at the right.
a) m  DQM =
b) m  DQY =
c) m  TQM =
d) m  TQS =
e) m  SQY =
f) m  DQT =
g) Name two right angles.
h) Name two obtuse angles that have QD as a side.
i) Name three acute angles that have QM as a side.
j) __________ bisects  MQS.
15. Name the following parts of isosceles ∆ABC.
a) legs
b) vertex angle
c) base angles
Q
16. Name the following parts for right ∆TMR.
a) right angle
b) hypotenuse
c) legs
17. Classify each triangle according to its angle measures and sides:
a) 17o, 80o, 83o
b) 44o, 83o, 53o
c) 25o, 65o, 90o
d) 45o, 45o, 90o
e) 60o, 60o, 60o
f)
10˚,10˚, 160˚
18. If mR = 2x + 7 and the measure of the supplement of R = x + 8, find mR.
19. If mNOM = 37 and mMOP = 73 find mNOP.
20. In this figure how many angles are adjacent to RST ?
21. Find the measure of the supplement of A if it is five times the measure of A.
22. If the measure of the complement of the angle is 10 less than ½ the measure of the supplement of the same
angle find the measure of the angle, its complement, and its supplement.
3
23. a) Find the restrictions on the third side of a triangle if the other two sides are 16 and 21.
b) Find the restrictions on x if the third side of a triangle is (2x-3) and the other two sides are 16 and 21.
24. If EF , EG , and EH are coplanar and EF is between EG and EH , then m  FEG + m  ______ = m  ______.
25. Complete each statement:
a) A triangle which has three congruent sides is an _________ triangle.
b) The _________ of a statement says the opposite of the original statement.
c) A triangle which has two congruent sides is an _________ triangle.
d) Two triangles are congruent if their _________ are congruent.
e) A geometric figure is congruent to itself by the _________ property.
f) If two sides of a triangle are congruent then the _________ opposite these sides are  .
g) Every equiangular triangle is an _________ triangle.
h) A _________ always contains the phrase if and only if.
i) Any point on the _________ of a segment is equidistant from the endpoints of the segment.
26. Write the reason each pair of triangles is congruent. SAS, ASA, SSS, AAS, HL, or none.
a)
b)
c)
d)
e)
f)
27. Find the missing angles and, where possible, the missing sides.
a)
b)
28. Classify each statement as true or false.
a) If 1 ≅ 2, then BA  BC .
b) If BCA ≅ BAC, then BA  BC
c) If BA = BC, then BD is the perpendicular bisector of AC .
d) If EA = EC, then BD is the perpendicular bisector of AC .
e) If BA = BC and EA = EC, then B, E, and D, are collinear.
29. Given: KM║NO
30. Given: MN║PO
4
Find: m  N
Find: all pairs of 
's .
31. If 4 ≅ 9, then _____ ║ _____
32. If a║b, then m1 =
33. If a║b, then m3 =
34. A pair of interior angles on the same side of
the transversal is:
35. A pair of corresponding angles is:
36. A pair of alternate interior angles is:
37. If DE ≅DF, mF =
38. Find x and mD.
39. 1 ≅ 2, mB = 100 o, and mC = 35 o.
Find: m1,
m2,
m3,
m4, and
mA.
40. Find x and mA.
41. If AE║BD, BF║CE,
m1 = 100 o,
then mDBF =
42.
43. Given: a║b, x =
45. m1 = m_____ + m _____
║XY, m2 =
44. If KM║NO, which angles are supplementary?
46. 2 is an exterior angle of which triangle?
5
47. If PQ║ST, mP = 48 o, mPRQ = 110o,
find mQ, mS, mT.
48. ║ m , find m1, m2, m3, m4, m5.
49. If EFG is a right angle, FHHG,
m2 = 40o, then mE =
50. If ║ m , m2 = 5x-9, m6 = 2x+18,
then find x and m2.
51. Find the following:
a) DA  DC
b) ED  EB
c) AC  DB
d) DE  EB
52. ABCD is a square.
Fill in all angle measures.
53. EFGH is a rhombus.
Fill in all angle measures.
54. JKLM is a rectangle.
Fill in all angle measures.
55. NOPQ is a parallelogram.
Fill in all angle measures.
56. RSTU is an isosceles trapezoid.
Fill in all angle measures.
57. A, B, C, and D are midpoints
of VY,VW,WX, and XY. If
VX = 20 and CD = 3, find BA,
WY, AD, and BC.
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58. If two sides of a triangle have measures 5 and 12, 59. If mA > mB > mC in triangle ABC, which side is
then the third side is between _____ and _____ .
largest?
60. Parallelogram ABCD. If mA = 5x-20
and mC = 3x, find x and mB.
61. If the perimeter of the parallelogram in #60 is 120
and AB = 4x+20 and BC = 6x-10, find x, AB, and AD.
62. The coordinates of A and B
are (2,7) and (-3,5), respectively.
Find the coordinates of the
midpoint of AB.
Find the slope of AB.
63. Show using slope that
ABC is a right triangle if
A(4,6), B(1,2), and C(5,-1).
64. If M is the midpoint of AB and
A(-3,-6) and M(1,-4), find the
65. Find the restrictions on x, given that the
mA  mC :
coordinates of B.
66. Write in slope-intercept form the equation of a
line passing through (1, 4) and (-2,2)
67. Given the point (-4,-2), find the coordinates of the
image point after each transformation:
a) reflect in the x-axis
b) reflect in the line y = 1
c) rotate 90 clockwise about the origin
d) roate 180 counterclockwise about the origin
68. Determine the number of lines of symmetry:
69. Give the most descriptive name for each quad.:
70. Write the converse, inverse, and contrapositive of: If it is warm today, then H-F will win.
71. A(2,6), B(8,-2), and C(-10,4).
Find the slope of the median to side:
a) AB
b) BC
c) AC
72. Use the same points and find the slope
of the altitude to side:
a) AB
b) BC
c) AC
7
d) write equation of median to AB
73. If M(-7,2) is the midpoint between A(8,1)
and B, find the coordinates of B.
d) d) write equation of altitude to AB
74. Prove ABCD is a
rectangle if
A(-2,3), B(8,3),
C(8,1), and D(-2,1).
75. Find the slope of
AC so that
mBCA is a
right angle if
B(-2,4) and C(6,1).
76. Given: KITE is a kite and KT is the  bisector of EI.
KI = 6x + 2y – 2,
IT = 2x + 3y
TE = 4x + 2y – 3,
KE = 3x + 4y.
Find: x, y, and the perimeter of KITE
PQR  STV.
PQ = x2, SV = 6,
ST = 2x + 15,
TV = 3 – x.
Find : a) All possible x values.
b) The perimeter of PQR.
c) Is PQR scalene, isosceles, or equilateral
77. Given:
78. What conclusion can be drawn from the following:
c  f , g  b, p  f , c  b
Other Topics to Review using problems the book (odds in back, evens listed)
(Chapters 1-3, 5, transformations, Section 15.2 triangle inequality)
Union and intersection (pg. 7 #5)
Most descriptive name for a quadrilateral (Coordinate proof) (pg. 258 #1, 4 [rectangle], 14 [rectangle], 28
[rhombus]
Systems/quadratics (pg. 164 #15, 16 [final answer = 2])
Transformations (CP book problems (packet sec 7.1#12,13,21,22, 35 and 7.4#25-28, 39-42)
All properties of quadrilaterals (Sections 5.4 – 5.7, checklist in notes)
All theorems/postulates/definitions (Notes throughout class)
More on parallel lines and angles (pg. 265 #7, 9, 18 [116.85 and no], 25)
All formulas (pg. 207 #9, 17)
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Honors Geometry: 1st Semester Final Exam Review…Proof Answers
1) 1. given 2. Draw AC; 2 pts det line 3. BD bis AC; If 2 pts on a line are =dist from seg endpts, then  bis.
4. AD ≅ AC; If a pt lies on bis, then it is = dist from seg endpts.
2) 1. given 2. OH  GJ; If altitude, then  3.  OHJ & OHG Rt ’s; If , then Rt. 4. OHJ ≅OHG; If Rt , then ≅
5. OH ≅ OH; Reflexive 6. GH ≅ JH; if median, then div into 2 ≅ seg 7. ΔGHO ≅ ΔJHO; SAS 8. G ≅ J; CPCTC
3) 1. Given 2. ED ║ AB; If ║ogram, then opp sides ║ 3. ACDE is a trap; If 1 pr opp sides ║ then trap
4. AE ≅ BD; If ║ogram, then opp sides ≅ 5. BD ≅ DC; If isos Δ, then legs ≅ 6. AE ≅ DC; transitive
7. ACDE is isos trap, If trap has 2 ≅ legs, then isos.
4) 1. Given 2. RS ≅ TO; If ║ogram, then opp sides ≅ 3. RS ║ TO; If ║ogram, then opp sides║
4. RSM ≅ PTO; If ║ lines, then alt ext ’s ≅ 5. ΔRSM ≅ ΔOTP; SAS 6. MR ≅ PO; CPCTC 7. RMS ≅ OPT ; CPCTC
8. MR ║ PO; If 1 pr opp sides ║ & ≅ then ║ogram
5) 1. given 2. XT ≅ VA; If rect, then opp sdies ≅ 3. TV ≅ TV; reflexive 4. XV ≅ TA; If rect, then diag ≅
5. ΔXTV ≅ ΔAVT; SSS 6. TXV ≅ VAT; CPCTC
6) 1. Given
2. AB ≅ AB; Reflexive
7) 1. Given
2. F ≅ J; If isos, then base ’s ≅
4. MF ≅ MJ; If isos, then legs ≅
8) 1. Given
10) 1. Given
4. DBA ≅ CAB; CPCTC
5. ΔABE is isos; If 2 ≅ ’s, then isos.
3. FH ≅ JG; If a seg is added to 2 ≅ seg, then sums ≅
5. OF ≅ KJ; If big seg ≅, then like div ≅
2. BAC & DCA are Rt ’s; If , then Rt.
5. ΔBAC ≅ ΔDCA; SAS
9) 1. Given
3. ΔDAB ≅ ΔCBA; SAS
6. ΔOFH ≅ ΔKJG; SAS
3. BAC ≅ DCA; If Rt ’s then ≅
7. OH ≅ KG; CPCTC
4. AC ≅ AC; Reflexive
6. B ≅ D; CPCTC
2. BC ≅ CE; If bisector, then 2 ≅ seg
2. AE ≅ ED; If sides ≅, then ’s ≅
3. BCA ≅ DCE; Vert ’s ≅
4. ΔBCA ≅ ΔDCE; AAS
5. AB ≅ ED; CPCTC
3. BEA ≅ CED; Vert ’s ≅ 4. ΔABE ≅ ΔDCE; ASA
9
Part II
1) 145º
2) a) S
b) N
c) A
d) S
3) mF = 140º
perimeter = 58
4) 110º
5) 64.5º
6) a) RHOM
b) PARA
c) RT Δ
d) SQUARE
7) 131º
8) 105º
9) 110º
10) 60
11) a) 2
b) lies on same line
c) lies on same plane
12) a) ray
e) line
b) seg
f) line, ray
c) seg
g) line, angle
d) seg
13) a) 40
c) 48
b) 15
d) 24
14) a) 60º
f) 90º
b) 150º
g) SQY, DQT
c) 30º
h) YQT, DQS
d) 30º
i) DQM, MQT, MQS
e) 90º
j) QT
15) a) BC & AB
b) B
16) a) R
c) A, C
18)
20)
22)
24)
25)
c) TR , RM
a) acute, scalene d) right, isosceles
b) acute, scalene e) equiangular, equilateral
c) right, scalene f) obtuse, isosceles
117º
19) 36º
4
21) 150º
20º, 70º, 160º
23) a) 5 < 3rd side < 37
FEH, GEH
b) 4 < x < 20
a) equilateral
e) reflexive
b) converse
f) ’s
c) isosceles
g) equilateral
d) corr ’s / sides ≅
i) perpendicular bisector
26) a) SSS
d) SAS
AB = 8
mBAC = 70º
b) mBAC = 75º mBCA = 60º
mD = 75º ; sides not possible
28) a) F
d) F
b) T
e) T
c) F
29) 65º
30) 2 ≅ 3
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41)
42)
43)
44)
45)
46)
47)
48)
49)
50)
p║q
16 (alt ext) or 13 (corr)
15 (corr) or 14 (alt int)
3 & 6 or 4 & 5
1 & 5 or 2 & 6
3 & 7 or 4 & 8
4 & 6 or 3 & 5
65º
59º
50º, 50º, 85º, 95º, 45º
52.5º, 22.5º
80º
80º
45º
O & KLO
N & MLN
3, 4
BDC
22º, 22º, 48º
55º, 50º, 55º, 50º, 130º
40º
9, 36º
51) a. ADC b.
b) TM
17)
b) ASA
e) ASA
c) SAS
f) HL
27) a) mABC = 55º mACB = 55º
h) bi-conditional
52)
DE or DEB c. E d. EB
All corner angles are 45º
All angles where diagonals intersect are 90º
53)
F
E
15°
15°
G
54)
75° 75°
75°
75°
15°
15°
H
All corner angles are 15º and 75º
All angles where diagonals
intersect are 30º and 150º
10
55)
Corner angles are 15º and 42º
Corner angles are 93º and 30º
All angles where diagonals
intersect are 45º and 135º
56)
Lower base angles are 15º and 42º
Upper base angles are 108º and 15º
All angles where diagonals
intersect are 30º and 150º
57) 3, 6, 10, 10
58) 7, 17
59)
60)
61)
62)
BC
10, 150º
5, 40, 20s
(-½, 6), 2/5
BD  1/5
AC and BD not opp reciprocals
75) BC  -3/8
AC  8/3
BC and AC are opp reciprocals
76) x = 4, y = 5, perimeter of KITE = 110
77) a) -3 b) 21 c) isosceles
78) p ~ g
Exam Notes
•
TBD minutes, at least 105
•
25 multiple choice @ 2pts = 50 pts
•
15 short answer @ 4pts = 60 pts
•
2 proofs @ 8 pts each
63) m AB = 4/3
m BC = -3/4
m AC = -7
AB  BC  B is a rt 
So ΔABC is rt Δ
64) (5,-2)
65) -12< x <-8
66) y 
2
10
x
3
3
67) a) (-4,2) b) (-4,4) c) (-2,4) d) (4,2)
68) 2, 3, 4
69) trapezoid, rhombus, rectangle, square
70) conv  If H-F will win, then it is warm today
inv  If it is not warm today, then H-F will not
win
contra  If H-F will not win, then it is not warm
today.
71) a) -2/15
b) 5/3
c) -7/12
d) y  
2
8
x
15
3
72) a) 3/4
b) 3
c) -6
d) y 
3
3
x
4
2
73) (-22, 3)
74) AD  undef
BC  undef
AB  0
DC  0
AC  -1/5
11