Download Geometry First Semester Final Exam

Geometry 1st Semester Final Review
1.
7. M is the interior of TOP. If
mTOM = 12.5 and mMOP = 16.5,
then mTOP =
.
A plane is determined by ….
2. The three undefined terms in geometry are ….
3. If H is the midpoint of TE and
TH = 11.22, then TE =
.
4. What is the measure of
C
CE ?
D
4x + 8
8. BD bisects  ABC, m  ABD = (7x – 1)  , and
m  DBC = (4x + 8)  . Find m  ABD.
27
E
6x
9. Use inductive reasoning to determine the next
three numbers in the following sequence:
1, -3, 5, -7, 9, …
5. Draw a plane with intersecting lines r and s and
line s contains three collinear points A, B, C.
10. What three items are next in the pattern?
11. Evaluate
6.
Solve:
2(4x – 3) –8 = 4 + 2x
3s 2  6r 2 , when s=5 and r=1
12. Use the distance formula to find BN.
17. Sketch a line that would have a zero slope.
N
y
7
6
5
18. Sketch a line that would have a undefined slope.
4
3
2
B
1
–7
–6
–5
–4
–3
–2
–1
1
2
3
4
5
6
7
x
–1
–2
–3
19. Write an equation of a line perpendicular to
y=
1
x + 4?
2
–4
–5
–6
–7
20. What is the equation of the line though (-1, 7)
and (4, -3)?
13. Given GH with endpoints G(-6, -6) and H(1, 2),
what are the coordinates of the midpoint?
21. Write an equation of a line parallel to
y=
14. What is the slope of the line through
(7, 6) and (3, -2)?
15. Sketch a line that would have a negative slope.
16. Sketch a line that would have a positive slope.
1
x + 2?
2
22. Determine whether the pair of lines
12x + 3y = 3 and y = 4x + 1 are parallel,
intersect, or coincide.
26. Find the measure of the supplement of  R,
where m  R = 132.6
23. l1 || l2, then …
27. Identify the hypothesis and the conclusion of
the conditional statement.
If it is raining, then the sun is not shining.
H:
which angles are corresponding angles and what is
their property?
C:
28. Write the logic symbolism for;
conditional statement:
which angles are alternate interior angles and what is
their property?
converse statement:
inverse statement:
which angles are same side interior angles and what is
their property?
contrapositive statement:
biconditional statement:
law of syllogism:
24. l1 || l2, find m1, if the m2 = 6x + 26, and m4
= 2x + 10.
29. Simplify the following ( a - e ):
a)
b)
c)
d)
25. Find the measure of the complement of  M,
where m  M = 32.6
125
98
3
2
72
e) ( 5)
2
30. Write the converse, inverse, and contrapositive
of the conditional statement:
If it is a horse, then it has 4 legs.
33. ∆ABC is an isosceles triangle. AB is the
shortest side with length 3x + 9.
BC = 8x – 8 and CA = 3x + 27. Find AB.
converse statement:
inverse statement:
34. One of the acute angles in a right triangle has a
measure of 41.7°. What is the measure of the other
contrapositive statement:
31. Classify ∆DAB by its angle measures, given
mDAB = 56  and mABD = 72  .
32. Classify ∆DBC by its angle measures, given
mBDC = 26  and mDCB = 51  .
acute angle?
35. Given that ∆ABC  ∆DEC and
mE = 47º, find mACB.
36. What is the m  CBA, if m  CAB = 26?
37. What is the value of x, if m  CBA = 6x?
38.
What is the mACD, if mABC = 37 ?
39.
AB = 16.5, AX = 7.9, and BC = 16.5. What is the
length of
44. Write a congruence statement for these
triangles, and name the postulate or theorem that
supports it.
AC ?
45. What can you use to prove
 ABE   CDE.
40. The circumcenter is equidistant from
the
of a triangle?
46. Classify
HG and EF .
41. The orthocenter of a triangle is the point of
concurrency of which lines?
42. The incenter is equidistant from the
of a triangle?
47. Given:
x?
 TUV   TWV.
What is the value of
43. Write a congruence statement for these
triangles, and name the postulate or theorem that
supports it.
48. List the sides of
to longest?
 ABC in order from shortest
B
75
A
50
55
C
49. . List the angles of
smallest to largest?
 GHJ in order from
54. Given that YW bisects  XYZ and
WZ = 14.3, find WX.
50. Find the measure of ‘x’.
55. Tell whether a triangle can have sides with
lengths 4, 2, and 7.
122
56. HK and
x
JK are angle bisectors of ∆JHI.
51. Find the measure of ‘x’.
3x - 17
Find m HIJ .
2x - 5
x + 40
57.
HK and JK are angle bisectors of ∆JHI.
52. Find the measure of  BCA.
Find the distance from K to
58.
53. In ∆ABC, ZC, YB, and XA are the medians of
the triangle. BY = 6.6, find BO.
C
X
Y
O
B
Z
A
JI .
What is the orthocenter of this triangle?
59. Find the values of x and y. Express your
answers in simplest radical form.
64. Find the two missing side lengths.
30
60
8
60. Find the value of x. Express your answer in
simplest radical form.
65. Find the missing side.
4
61. . The vertices of square ABCD are the midpoints
of the sides of a larger square. Find the perimeter
and the area of square ABCD. Round to the nearest
hundredth.
5
66. A painter leans a 15 foot ladder against a house.
The base of the ladder is 5 feet from the house. To
the nearest tenth of a foot, how high on the house
does the ladder reach?
ABC with AB = 22, find the length of
midsegment XY .
62. Given
67. Find the length of each leg.
12
45
63. Find the two missing side lengths.
68. Find the missing side lengths.
5 3
60
30
3 2
45