Download Semester Exam Review

Semester Exam Review
Name________________
Period____
Honors Geometry 12-13
Classify each statement as always, sometimes or never true.
1.
2.
3.
4.
5.
6.
Three points lie on exactly one line.
Three points lie on exactly one plane.
Two intersecting lines lie on exactly one plane.
A line and a plane intersect in exactly one point.
Three noncollinear points lie on two planes.
Two planes intersect to form exactly one point.
7.
DE and EF are opposite rays.
8. *Point E lies between D and F. DE= 2x 2 , EF  7 x , and DF = 4. Find the value of x.
9. * HB and HC trisect AHD . Such that mBHD  mCHD Thus AHD is divided into 3
congruent angles. HD bisects BHE . If mBHC  32 , find mCHE .
10. *Let E be the midpoint of AC and E also be the midpoint of RS . AE=2x, EC = 16, RE = 2x+3y,
and ES = x+26. Find the values of x and y.
Provide a counterexample to show that each statement is false.
11. If D, E, and F are collinear, then DE + EF = DF.
12. If xy  5x , then y>5.
13. x 2  25 if and only if x = 5.
14. A figure is a rectangle if and only if it is a parallelogram.
15. An angle has a measure of 100 degrees if and only if it is an obtuse angle.
16. Write the converse of the following statement and determine if the converse is true or false.
If BA=BC, then A is between B and C.
17. *A complement of an angle is four times as large as the angle. Find the measure of the angle.
18. *The measure of a supplement of an angle is 6 more than twice the measure of a complement
of the angle. Find the measure of the angle.
19. *The coordinates of F and E are -4 and 16 respectively. C is the midpoint of ̅̅̅̅ and D is the
midpoint of ̅̅̅̅ . Find FD.
20. *Find the values of x and y in the diagram at the right.
(5y-20)°
(x²+10)°
26°
Use the picture at the right to determine which lines if any must be parallel based on the given
information.
a
b
e
21. _______ 2  5
2 1
5 6 7
22. _______ m4  m17  180
10 9 8
4 3
23. _______ m6  m7  m1  m13
24. _______ m17  m18  m10
17 18 19
22 21 20
16 13
15 14
c
d
Find the values of the variables in the pictures below.
25. *
70⁰
(2x-10)⁰
26. *
27. *
40⁰
5y⁰
5y⁰
2x⁰
60⁰
(x-y)⁰
71° y° 63°
28. *Find the sum of the measures of the interior angles of a convex heptagon.
29. *Find the measure of each interior angle of a regular dodecagon.
30. *The measure of each interior angle of a regular polygon is 6 times that of each exterior angle. How
many sides does the polygon have?
31. *The vertices of ABC have coordinates A(-1,2), B(5,2), and C(1,5). Given G(5,3) and H(11,3), find
all possible locations of I so that ABC  GHI .
Determine if the following triangles can be proved congruent. If so list the postulate that can be used.
32.
33.
34.
35.
60⁰ 60⁰
Find the value of x in the pictures below.
18⁰
36.
37.
35⁰
x⁰
x⁰
60⁰ 60⁰
38. *Find the equation of the line in slope-intercept form that contains the altitude from A of the
triangle with vertices of A(3,2), B(-1,6) and C(-5,-3). Put your answer in slope-intercept form if possible.
39. *Find the equation of the line in slope-intercept form that contains the median from C of the
triangle with vertices of A(3,7), B(0,-2) and C(8,5). Put your answer in slope-intercept form if possible.
40. *Find the equation in slope-intercept form of the perpendicular bisector of AB given the triangle
with vertices of A(-3,-5), B(4,-2) and C(5,5). Put your answer in slope-intercept form if possible.
Determine if the following quadrilaterals can be proven to be parallelograms. If your answer is yes,
provide the reason
41.
42.
43.
Use the picture at the right to answer the following questions.
44. AC=
45. mBFD =
C
B 71⁰
46. mCAE =
19
8D
A
16
F
29
65⁰
E
Write a two-column proof for the following.
47. Given: 1  2 , O is the midpoint of DB
A
1
Prove: ABCD is a parallelogram
B
O
2
D
48. Given: AD BC; AD  BC
C
D
Prove: AB  CD
C
1
2
A
B
49. Given: GK bisects JGI ; mH  m1
Prove:
J
GK HI
G
H
2
1
K
I
50. Given: m1  m2
C
AD bisects CAB
BD bisects CBA
D
Prove: m3  m4
A
1
3
4
2
B
C
51. Given: A  B; AD  DB
Prove: CD bisects ACB
A
Constructions:
52. Construct AB  CD
B
A
53. Construct 1  2
1
D
B
54. Construct the perpendicular bisector of AB
B
A
55. Construct line k through point P that is parallel to m.
P
m
56. Construct BD that bisects ABC .
A
B
C