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Geometry CP
Midterm Review Chapter 2
Describe the pattern and give the next number or picture in the pattern.
1. -3, 3, 9, 15,…..
2. 21, 12, 3, -6,…
Name_______________________________
3.
Decide if the statement is false. If false, provide a counterexample.
4. A line can be in more than one plane.
5. If
, then Y the midpoint of
.
6. If
the supplement of
7. Supplementary angles are always
adjacent.
9. Through any two points, there exists
exactly one line
8. If two planes intersect, then their
intersection is a point.
, then the measure of
.
Write the converse, inverse and contrapositive of each statement. Then tell whether each statement is true or false.
10. If a polygon is a rectangle, then it is a
11. If the measure of an angle is less than 12. Two lines that intersect form two
parallelogram.
pairs of vertical angles.
, then the angle is acute.
Converse:__________________________
Converse:__________________________
Converse:__________________________
__________________________ T or F
__________________________ T or F
__________________________ T or F
Inverse:___________________________________
Inverse:___________________________________
Inverse:___________________________________
_________________________________T
_________________________________T
_________________________________T
or F
Contrapositive:______________________________
_________________________________
T or F
or F
Contrapositive:______________________________
_________________________________
T or F
or F
Contrapositive:______________________________
_________________________________
T or F
Rewrite the statement as a conditional in if-then form. Then write the statement as a biconditional statement.
14. Three points are collinear if there is a 15. All high school students take three
13. The measure of a right angle is
.
line containing them.
math courses.
If-Then ___________________________
If-Then ___________________________
If-Then ___________________________
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
Biconditional :_____________________
Biconditional :_____________________
Biconditional :_____________________
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
Decide whether each statement about the diagram is true. Explain you answer.
16.
is perpendicular to
17.
and
are complementary
18.
bisects
Make a valid conclusion about the situation.
19. If it is a weekday, Trisha is at school.
20. If two angles have the same measure,
Today is Wednesday.
then they are congruent.
.
21. If a person is born in the U.S., he or
she is a U.S. citizen. Taylor was born in
New Jersey.
Use the Law of Syllogism to write the statement that follows from the pair of statements given.
24. If you pass a driver’s test, then you
22. If a triangle has a
angle, then it is a 23. If you like so study history, then you
like
to
read
books.
If
you
like
to
read
can drive a car. If you can drive a car,
right triangle. If a polygon is a right
books,
then
you
enjoy
going
to
the
library.
then you must act responsibly.
triangle, then the two acute angles are
complementary.
Use the Law of Detachment to make a valid conclusion in the true situation.
25. If two angles are right angles, then they 26. If Nathan is enrolled at North High
School, then Nathan has and ID number.
are congruent.
and
are right
Nathan is enrolled at North High School.
angles.
State which postulate justifies each statement.
29. If M is between X and Y, then
28. If D is in the interior of
, the
XM + MY = XY.
.
Solve for y in each equation and justify each step.
31.
32.
Steps
Reasons
Steps
27. If an angle measures more than
then it is not an acute angle.
.
30. Find the measure of MN if N is
between M and P, MP = 6x-2, MN = 4x,
and MP = 16.
33.
Reasons
Steps
Reasons
Use a property of equality to complete the statement and then state the property used.
35. If AB = CD and CD = TU, then
36. If RS = WX, then
34. If
, then
_________=_________
______ + AB = _____ + AB
________
37. If
and
38. If BC = RL, then RL = _____
; then
Name the property illustrated by the statement.
40.
41. If
, then
,
39. If
then
,
42. If
and
, then
Write a proof for the following.
43. Given: RT = SU
Prove: RS = TU
Statements
1.
2.
3.
44. Given: AB = CD
Prove: AC= BD
Reasons
1.
2.
3.
Statements
1.
2.
3.
46. Given:
Prove:
47. Given:
45. Given:
Prove:
Reasons
1.
2.
3.
and
and
are complements
are complements
Statements
1.
2.
3.
48. Given:
Prove:
Reasons
1.
2.
3.
Statements
1.
2.
3.
4.
5.
Reasons
1.
2.
3.
4.
5.
Prove:
Statements
1.
2.
3.
Reasons
1.
2.
3.
Statements
1.
2.
3.
Reasons
1.
2.
3.
Find the value of x and y in each problem.
50.
49.
51.
For the following: ER  LV and OM  GT and mGOE  47
52.
mGOM =_________
53.
mROT =_________
G
54.
mLOR =_________
55.
E
M
mTOL =_________
L
V
O
56.
mLOG =_________
57.
mVOT =_________
R
58. mMOE =_________
59. mMOR =_________
For the following: 1 is a right angle and m6 = 36°.
Complete the statement with <, >, or =.
60. m6  m7 __?__ m4  m5
61. m6 + m8 __?__ m2 + m3
62. m9 __?__ 3(m6)
63. m2 + m3 __?__ m1
T
Use the diagram to answer the following.
64. If
65. If
, find
, find
and
and
.
.