GEOMETRY FINAL REVIEW-ch.2

1
GEOMETRY FINAL REVIEW-ch.2

• Which term best defines the type of reasoning
  used below?
• Abdul broke out in hives the last four times
  that he ate chocolate candy. Abdul concludes
  that he will break out in hives if he eats
  chocolate.
•  
• Inductive
• Deductive
• Converse
• Inverse

• a) Inductive

2
GEOMETRY FINAL REVIEW-ch.3

• LJ and GH are parallel and
• mlt L 40.
• Find the measures of the numbered angles.

• mlt 1 ______
•  
• mlt 2 ______
•  
• mlt 3 ______
• ANSWER
• mlt 1 100
•  
• mlt 2 40
• mlt 3 140

3
GEOMETRY FINAL REVIEW-ch.3

• In the figure below,
• mlt3 mlt5 180. Determine which lines are
  parallel. Justify your reasoning.
•  

• Line r is parallel to line s.
• Justifications may vary. One approach to
  justification converse of same side interior
  angles theorem

4
GEOMETRY FINAL REVIEW-ch. 2

• The given statement is a valid geometric
  proposition.
•  Statement If a triangle has two congruent
  angles, then it is an isosceles triangle.
•    a) Write the contrapositive of this
  statement
•  
• b) NOW, Determine if the contrapositive
  statement is valid. Explain your reasoning.

• a) If a triangle is not isosceles, then the
  triangle does not have two angles that are
  congruent.
• b) The contrapositive statement is valid. The
  triangle could be equilateral, which is also
  isosceles. It could also be scalene, with no
  congruent angles. Also, the contrapositive of a
  true statement is always true. If a statement is
  false, its contrapositive will be false also.

5
GEOMETRY FINAL REVIEW-ch. 2

• The given statement is a valid geometric
  proposition.
• Statement If a quadrilateral is a kite, then
  its diagonals are perpendicular.
•    Which of the following is the inverse
  statement?
• a) If a quadrilateral has diagonals that are
  perpendicular, then it is a kite.
• b) If a quadrilateral is not a kite, then its
  diagonals are not perpendicular.
• c) If a quadrilateral has diagonals that are not
  perpendicular, then it is not a kite.
• d) If a quadrilateral is a kite, then its
  diagonals are not perpendicular

• B

6
GEOMETRY FINAL REVIEW-ch. 5

• Which is the correct construction of a
  perpendicular bisector of AB?

• C

7
GEOMETRY FINAL REVIEW-ch. 3

• C

• Which is the correct construction of a line
  segment parallel to AB passing through point C?

8
GEOMETRY FINAL REVIEW-ch.1

• Complete the following statements.
• a) The ceiling and floor of your kitchen are
  examples of __________planes.
•  
• b) A wall and the floor of your kitchen are
  examples of _____________planes.
• Word choices
• Coplanar
• Parallel
• Skew
• Perpendicular

1. Parallel
2. Perpendicular

9
GEOMETRY FINAL REVIEW-ch.1

•  Complete the following statement Two lines
  that do not lie in the same plane are called
  ________________ lines.
•  a) Coplanar
• b) Parallel
• c) Skew
• d) Perpendicular

• C

10
GEOMETRY FINAL REVIEW-ch. 5

• In ?ABC, point I is the incenter.
• m lt BAI x 4
•  
• m lt IAC 2x 6
•  
• Find the value of x.

• x10

11
GEOMETRY FINAL REVIEW-ch. 5

• C

• ?LPT is an obtuse scalene triangle. If P is the
  obtuse angle in the triangle, which of the
  following is not a valid conclusion?
• a) mlt L m lt T lt m ltP
• b) mlt L m ltT lt 90
• c) mlt L mlt T 90
• d) m lt L m lt T m lt P 180

12
GEOMETRY FINAL REVIEW-ch. 5

• Which triangle has an altitude that is also a
  median?
•  

13
GEOMETRY FINAL REVIEW

• One approach to the justification
• ltE ? ltD and AE ? CD Given
• lt GJF ?ltLJK Vertical angles are
  congruent.
• ? GHJ ? ? LKJ AAS
• AB ? CB Corresponding Pts of Congr. ?s are
  Congruent (CPCTC)
•  

• In the diagram below, ltE ? ltD and AE ? CD.
  Prove AB ? CB using mathematical language and
  concepts.

14
GEOMETRY FINAL REVIEW-ch. 1

• In the triangle below, how long is AC?
• 6
• 9.1
• 10
• 14.1  B(7,5)
•  
•  
• A(-2,-3) C(7,-2)
•  
•  
•  
•  

• B

15
GEOMETRY FINAL REVIEW-ch. 8

•  

• A

16
GEOMETRY FINAL REVIEW-ch. 8

•  

• D

17
GEOMETRY FINAL REVIEW-ch. 8

• What is the mlt R, to the nearest degree, in the
  figure below?
• A) 60
• B) 36
• C)30
• D) 27

• A

18
GEOMETRY FINAL REVIEW-ch. 8

• At a distance of 20 m from a building, a person
  who is 3 m tall looks up at an angle of 25 to
  see the top of the building. How tall is the
  building to the nearest meter?(HINT Draw a
  picture)
• A)8 m
• B) 9 m
• C) 12 m
• D)18 m

• B

19
GEOMETRY FINAL REVIEW-ch. 8

• Find the length of the hypotenuse, to the nearest
  tenth of a centimeter, of a right triangle if one
  angle measures 70 and the adjacent leg measures
  8 cm. (HINT Draw a picture)

• 23.4 cm

20
GEOMETRY FINAL REVIEW-ch. 8

• Find the value of a in the figure below, to the
  nearest whole number.
•  A) 10
• B) 11
• C) 14
• D) 16

• B

21
GEOMETRY FINAL REVIEW-ch. 6

• In the parallelogram below,
• WV 5x 2 and YV -x 20. Find WY.
• A) 17
• B) 20
• C) 34
• D) 50

• C

22
GEOMETRY FINAL REVIEW-ch.6

• In the parallelogram below,
• m lt ABC 70. Find m lt ACD.

• mltACD65

23
GEOMETRY FINAL REVIEW-ch.6

• The perimeter of the figure below is 48. Find
  the value of x.

X7
24
GEOMETRY FINAL REVIEW-ch. 6
Complete the proof of the following statement
If the diagonals of a quadrilateral bisect each
other, then the quadrilateral is a
parallelogram. Given AC and BD bisect each
other. Prove ABCD is a parallelogram.

•  

 
SAS
 
Converse of
ABCD is a parallelogram.
25
GEOMETRY FINAL REVIEW-ch. 11

• A trapezoidal prism has ____ total faces.
• A) 4
• B) 5
• C) 6
• D) 7

• A)4

26
GEOMETRY FINAL REVIEW-ch. 11

• If a plane intersects a cube, the intersection of
  the plane and cube cannot be a(an) ___________.
• a) Triangle
• b) Square
• c) Rectangle
• d) Octagon

• d) Octagon

27
GEOMETRY FINAL REVIEW-ch.1

• AC starts at point A (1,4), and ends at point C
  (7, 13). What are the coordinates of the
  midpoint of AC?

• (4, 8.5)

28
GEOMETRY FINAL REVIEW-ch.1

• Given points A (0, -3), B (5, 3), Q (-3, -1),
  which of the following points is a location of P
  so that PQ is parallel to AB?
• a) (0,3)
• b) (12,5)
• c) (-7,11)
• d) (2,5)

• d

29
GEOMETRY FINAL REVIEW-ch.12

• Suppose triangle ABC has vertices A (-5,-2), B
  (-6,-2), and C (-6,-6). If triangle ABC is
  rotated 90 counterclockwise about the origin,
  what are the coordinates of the vertices of
  triangle ABC? (HINT use your reasoning
  skills)
• A (2,-5), B (2, -6), C (6, -6)
• A (-5,2), B (-6,2), C (-6,6)
• c) A (5,-2), B (6,-2), C (-6,-6)
• d) A (2,-5), B (-2,-6), C (-6,-6)

• a

30
GEOMETRY FINAL REVIEW-ch.12

• How many lines of symmetry does the polygon shown
  have?
• a) 0
• b) 1
• c) 2
• d) 3

• 1

31
GEOMETRY FINAL REVIEW-ch. 10

• Find the area of the sector in circle P if PA
  10 cm and measure of arc APB 36.
• a) 10p cm2
• b) 20p cm2
• c) 36p cm2
• d) 72p cm2

• a

32
GEOMETRY FINAL REVIEW-ch. 10

• Find the area of the shaded region.

• Area of square 256 cm2 (1616)
• Area of circle 64p cm2
• (82)
• Area shaded region
• 256 - 64p cm2
• or
• approx. 55.04 cm2

33
GEOMETRY FINAL REVIEW-ch. 10

• b

• In circle P, find the area of the shaded region.
  Use an approximate value of 3.14 for p.
•  
• a) 3.14 square units
• b) 4.56 square units
• c) 6.28 square units
• d) 9.62 square units

34
GEOMETRY FINAL REVIEW-ch. 10

• In circle Q, find the measure of arc ADB.
•  
•  
• a) 42
• b) 138
• c) 222
• d) 318

• c

35
GEOMETRY FINAL REVIEW-ch. 10

• In circle P, find the length of
• arc AB if PA 10 and
• mltAPB 36.
•  
• a) 2 p
• b) 0.556 p
• c) 10 p
• d) 12 p

• a

36
GEOMETRY FINAL REVIEW-ch.10
What is the length of the apothem of a regular
hexagon with side length 8 m ? What is the area
of the hexagon?

•  

37
GEOMETRY FINAL REVIEW-ch. 10

•  
• The area of a sector of a circle is 54 p cm2. If
  the central angle is 60, what is the radius of
  the circle?

• Radius 18 cm

38
GEOMETRY FINAL REVIEW-ch. 11

• Two cylinders have the same height. Their radii
  are 6 cm and 3 cm. What is the ratio of the
  volume of the cylinder with radius 6 cm to the
  volume of the cylinder with radius 3 cm?

• 81

39
GEOMETRY FINAL REVIEW-ch.11

• If the volume of a cone is 96 p cm 3 and the base
  of the cone has a radius of 6 cm, find the height
  of the cone.
•  
• 2.55 cm
• 8 cm
• 16 cm
• 48 cm

• b

40
GEOMETRY FINAL REVIEW-ch. 11

• Donna wants to put a ceramic castle whose volume
  is 350 cm3 and a plastic scuba diver whose volume
  is 250 cm3 in her aquarium as decoration. Her
  aquarium measures 40 cm X 30 cm X 30 cm high.
  The water is 2 cm from the top before she begins
  to decorate. How much will the water rise when
  she puts the castle and the diver in?
•  0.5 cm
• 1 cm
• 2 cm
• 6 cm

• a

41
GEOMETRY FINAL REVIEW-ch. 11

• Cube A has side lengths that are two times as
  long as the sides of cube B. How many times
  larger is cube As volume than that of cube B?
•  
• 2
• 4
• 6
• 8  

• d

42
GEOMETRY FINAL REVIEW-ch. 2 ch. 6

• Consider these statements
• Every square is a rhombus.
• Quadrilateral ABCD is not a rhombus.
•  
• Which of these conclusions can be made using both
  statements?
• ABCD is not a parallelogram.
• ABCD is a rectangle.
• ABCD is not a square.
• ABCD is a trapezoid

• c

43
GEOMETRY FINAL REVIEW-ch. 2

• Melanie, Nikki, and Donny are three students in a
  geometry class. Melanie is younger than Nikki,
  and Donny is older than Nikki.
• Which of these must be true?
•  
• Donny is the youngest of the three students.
• Melanie is the youngest of the three students.
• Nikki is the oldest of the three students.
• Melanie is the oldest of the three students.

• b

44
GEOMETRY FINAL REVIEW-previous course

• If the pattern shown below continues, how many
  squares will be in the next figure?
•  
•  
• 6
• 8
• 16
• 64

• d

1 8 2 16
4 32
45
GEOMETRY FINAL REVIEW-ch. 2

• The two statements below are true.
• All simkos are temas.
• All bollies are simkos.
•  
• Using deductive reasoning, which of these
  statements must also be true?
•  
• All temas are bollies.
• All simkos are bollies.
• All temas are simkos.
• All bollies are temas.  

• d

46
GEOMETRY FINAL REVIEW-ch. 5

• Given AF ? FC
•  
• Use the word bank below the triangle to name each
  special segment in ?ABC.
•  
• Word Bank Median, Angle Bisector, Perpendicular
  Bisector, Altitude
•  
• BF ______________  
• FG _______________

• BF Median
• FG Perpendicular Bisector

47
GEOMETRY FINAL REVIEW-ch. 5

• Given ABE ? EBC. Use the word bank below the
  triangle to name each special segment in ?ABC.
•  
•  
• Word Bank Median, Angle Bisector, Perpendicular
  Bisector, Altitude
•  
• BD _____________ 
• EB ______________

• BD Altitude
• EB Angle Bisector

48
GEOMETRY FINAL REVIEW-ch.3 and ch. 4

• Jennifer has created a two-column proof as a
  response to the following question. Evaluate her
  argument to determine if you support or
  contradict her conclusion.
•  
• Given LA ?PS, LS ?PA Prove LA ll
  PS
•  
•  Statement Reason
• LA ? PS 1) Given
• SL ? AP 2) Given
• SA ?AS 3) Same Segment/Reflexive
• ?LAS ??PSA 4) SSS
• ?PSA ?? LSA 5) Corresponding Parts of
  Congruent Triangles are Congruent
• LA ll PS 6) Conv. Alt. Interior angles Thm
•  
• Determine if Jennifers argument is valid.
  Explain your reasoning. Support your answer with
  evidence from the diagram or Jennifers proof.

• Jennifers argument is not valid. On step 5 of
  her proof, she states that ?PSA ? ?LSA. This
  would indicate that LS ll PA and not LA ll PS.
  Jennifer should have stated that ?LAS ? ?PSA.

49
GEOMETRY FINAL REVIEW-ch. 11

• B

50
GEOMETRY FINAL REVIEW-ch. 1 and ch. 4
 

51
GEOMETRY FINAL REVIEW-ch. 1

• Z(-6,1)

52
GEOMETRY FINAL REVIEW-ch.5

• D

53
GEOMETRY FINAL REVIEW-ch.10

•  

• Calculate the area of the trapezoid.