Download Geometry Chapter 3 Exam

MIDTERM REVIEW
Name:________________________
Show all your work!
Date:____________Period:_______
For 1-12, justify each statement with a Geometry Rule
D
1. mAXB = mEXF
C
2. AX + XE = AE
E
3. mBXE + mEXF = 180
4. If BF  DX, then BXD  DXF
F
B
5. If X is the midpoint of BF, then BX = XF.
X
A
6. If BF  DX, then DXE and EXF are complementary.
7.
If XC bisects BXD, then
1
mBXC = mBXD.
2
8. mAXB + mBXC = mAXC.
9.
If BXC and CXD are complementary, then
mBXC + mCXD = 90
10.
11.
If BF  DX, then BXD is a right angle
If BXC and CXF are supplementary,
then mBXC + mCXF = 180
12. If X is the midpoint of AE ,
then AX = ½ AE
For #13, write an equation and solve for the angles.
13. The sum of an angle’s complement and twice its supplement is 324°. Find the angle, its complement, and
its supplement.
For #14 give a one-word response that best describes the answer:
14.(a)
(b)
(c)
(d)
the supplement of an acute angle is ______________
the complement of an acute angle _____________
the supplement of an obtuse angle is ______________
the supplement of a right angle is ____________
For #15-16, refer to the diagrams and solve for all unknowns.
15. Solve for x, mABC, mDBE
16. Solve for x, mFGH, mHGI
A
H
D
4x - 27
B
3 + 2x
C
8x - 40
E
F
2x + 20
I
G
For #17, refer to the diagram to complete the question:
17. (a) Name a straight angle
W
O
3
(b) Name two adjacent angles.
2
Z
1
(c) Name an acute angle.
X
(d) Give another name for angle 2.
(f) What two angles add together to create XOZ ?
(e) Give another name for WO
For #18, complete the proof:
18. Given:
BA = CA
BX = CY
A
Prove: XA = YA
X
Y
C
B
1.
2.
1.
BA = BX + XA
CA = CY + YA
3.
4.
5.
Given
2.
3.
BX = CY
Y
Substitution
4.
5.
For 19-21, complete with always, sometimes, or never.
19. Alternate interior angles are _____________ congruent.
20. Vertical angles are __________ congruent.
21. Corresponding angles are ___________ congruent.
For 22-24, refer to the diagram:
22. Name two pairs of alternate interior angles
1 2
4 3
23. Name three pairs of corresponding angles
5 6
8 7
24. Name two pairs of same-side interior angles
For #25, complete the proof:
25. Given: 2  6
Prove: l m
1 2
4 3
l
6
5
8
7
m
Statements
Reasons
1. ________ 2  6 ___________
1.
2. _________ 2  4 __________
2. __________________________
3. ___________________________
3. __________________________
4. ___________________________
4. __________________________
Given___________
For #26-27, classify the triangles based on their sides and angles.
27. The perimeter of ABC is 36. Is the triangle
equilateral, isosceles, or scalene?
26.
8x - 20
B
3x + 1
2x + 2
3x + 5
2x
A
4x - 3
C
For #28, l m . Write two equations and
solve for x and y.
For #29, find the following:
29. (a) each exterior angle of a hexagon
28.
(b) each interior angle of a pentagon
2x + 40
(c) sum of the interior angles of an octagon
5y + 20
x + 80
(d) each interior angle of a decagon
For #30-32, name a triangle congruence and the postulate you would use to show that the triangles are
congruent.
30.
F is the midpoint of EH
31. JM  LK , LJ  KJ
32.
ED HG
B
J
E
G
A
60
61
F
60
D
H
L
K
M
M
N
B
For #33-34, complete each proof:
33.
Given: CD bisects BCJ and BDJ
Prove: BD  JD
C
3
4
2
1
59
D
J
1.__________________________
1.__________________________
2.__________________________
2.__________________________
__________________________
3.__________________________
3.__________________________
4.__________________________
4.__________________________
5.__________________________
5.__________________________
34. Given: WX ZY , WY ZX
W
X
3
Prove: WX  ZY
1
Y
1.__________________________
2
4
Z
1.__________________________
2.__________________________
__________________________
2.__________________________
3.__________________________
3.__________________________
4.__________________________
4.__________________________
5. _________________________
5. __________________________
35. List three examples of undefined terms: _________, __________, __________
36. List three examples of defined terms: _________, __________, __________
37. Which of the following describes deductive reasoning:
A.
B.
C.
D.
E.
using logic to draw conclusions based on accepted statements
accepting the meaning of a term or definition
defining mathematical terms to correspond with physical objects
inferring a general truth by examining a number of specific examples or pattern
none of the above
38. Which of the following describes inductive reasoning:
A.
B.
C.
D.
E.
using logic to draw conclusions based on accepted statements
accepting the meaning of a term or definition
defining mathematical terms to correspond with physical objects
inferring a general truth by examining a number of specific examples or pattern
none of the above
A
B
1
10
F
9
11 8
7
E
2 3
5
4 C
6
D
39. If 9  5 , name a pair of segments
that must be parallel: ______________
40. If AB FC , name a pair of angles
that must be congruent: ______________
For #41 – 44, draw a separate triangle for each question and illustrate each special segment:
41. altitude
42. median
43. angle bisector
45. If AH is the median to MT , find MH.
MH  6 y  3
HT  3 y  15
44. perpendicular bisector
A
M
T
H
For #46-47, answer the questions about parallelograms:
46. Quadrilateral LEXI is a parallelogram.
Find the values of a, b, x, and y.
2a - b
E
X
46
2y
6
a+b
3x - 2
L
I
9
47. ABCD is a parallelogram.
C
B
a.) If BX = 2x + 8 and BD = 48, then x = ______
X
b.) If m<ADC = 80, and m<DCB =
2x – 6, then x = _____
48. (a) Solve by Addition/Subtraction
A
(b) Solve for x. A  C
D
3x – 3y = 6
2x + y = -5
B
x+ 3
3x - 7
C
A
13
For #49-58, write the letter of every special quadrilateral that has the given property.
A Parallelogram
B Rectangle
C Rhombus
D Square
E Trapezoid
49. All angles are right angles.
49. __________
50. Both pairs of opposite sides are congruent.
50. __________
51. Diagonals are congruent.
51. __________
52. Diagonals are perpendicular.
52. __________
53. Diagonals bisect each other.
53. __________
54. Exactly one pair of opposite sides is parallel.
54. __________
55. Both pairs of opposite sides are parallel.
55. __________
56. Both pairs of opposite angles are congruent.
56. __________
57. Equiangular but not equilateral.
57. __________
58. Equilateral but not equiangular.
58. __________
For #64-65, solve the proportion for x.
59.
x3 4

2
3
61.)
3x3  48 x
2 x 2  5 x  12
60.
3 x  5 18 x  5

3
7
 25a 2b5  16 x 2 y8 
62.) 

3 
3
 12 xy  15a b 
63.)
x3  3x 2  x  3
x3  x 2  9 x  9
For #64 – 67, solve for x and y (where x and y are positive):
64.)
65.)
12
16
6
7
x
y
9
x
12
24
66.)
67.)
15
12
x
5
24
10
9
x
For #68 – 69, solve for x:
68.)
x2 4

x3 5
69.)
x 1
x4

x2 x2