Download Geometry Midterm Review 2016

1st Semester Midterm Review
Geometry Midterm Review
2016-2017
Mr. Pisciotta
Chapter 1: Essentials of Geometry
Sections 1.1 – 1.5
1.1
Points, Lines and Planes
1.2
Use segments and Congruence
1.3
Midpoint and Distance Formulas
-Be able to graph a line given an equation
-Find the distance and midpoint between any two points on a line segment or graph
1.4
Measure and Classify Angles
1.5
Angle Pair Relationships
a) Parallel lines cut by a transversal
b) Angles created by a transversal
1.5
Constructions:
a) Construct an angle bisector
b) Construct a segment bisector
DEFINITIONS:
Congruent segments
Congruent angles
Midpoint
Angle bisector
Vertical angles
1st Semester Midterm Review
Complementary
Supplementary
Perpendicular lines
Parallel lines
POSTULATES:
Point, Line and plane postulates (as covered in review)
Segment addition
Angle addition
Linear Pair postulate
PROPERTIES
Multiplicative Inverse
Reflexive a=a
Symmetric a=b then b=a
Transitive: if a = b and b = c, then a=c
Substitution: If a = c, then a can be substituted for any value c
Distributive: a(b+c)=ab+ac
Chapter 2: Reasoning (logic) and Proof
Sections 2.1, 2.2, 2.5
2.1
Inductive Reasoning
2.2-2.5 Analyze Conditional Statements
a) converse
b) inverse
c) contrapositive
1st Semester Midterm Review
d) biconditional
e) know the truth values (if p then q, etc…)
2.6
Algebraic Proofs
a) formal two column proof
b) Algebraic properties/definitions
The following is intended to give the student an accurate idea of what type of skills are required for the
midterm exam for Tuesday 12/13/16. The exam is worth a MINIMUM of 150 points and will replace a
lower test grade. Be sure you can work all of the problems accurately. If not, ask for help!
Choose the best answer for each question.
1. Find the length of the segment with endpoints L(-1, -3) and M(-6, 9).
A. 13
B. 17
C. 5
D. 12
2. Points A, B and D
A. determine a plane
F
B. are collinear
C. are contained in only plane P
C
D. are noncoplanar points
A
P
E
D
B
G
R
3. What is the intersection of planes P and R.
A points A, D and B
B. AB
C. AB
D. AD
4. What is the measure of QT if R is between Q and T, QR = 14 and RT = 5?
A. 10
B. 11
C. 19
D. 9
5. Find the coordinates of the midpoint of the segment with endpoints D(6, 6) and E(-2, 2).
A. (3, 4)
B. (2, 4)
C. (4, 8)
D. (1, -1)
6. What are the sides of 5 ?
A. WG and WF
B. AB and WF
E
D. WB and WF
1 8 9
C 2
B
C. WB and WG
3
4
W
5
F
6
G
A
7
1st Semester Midterm Review
7.
5 and 6 are
A. adjacent
8.
9.
B. vertical
C. supplementary
D. complementary
8 and 9 are
A. adjacent
B. vertical
C. supplementary
D. complementary
1 and 2 are
A. adjacent
B. vertical
C. complementary
D. linear pair
C. linear pair
D. complementary
10. 3 and 4 are
A. adjacent
B. vertical
11. Find m1 .
A. 25
C. 175
1
3x+10
2x+15
B. 155
D. 5
12. If mABD  40 and mABC  110 , find mDBC.
D
A
A. 150 B. 130
C. 70
D. 80
B
C
13. Find mRSU if ST bisects RSU , m1  4 x  12 and m2  2 x  6.
A. 48
B. 18
C. 9
D. 24
14. Choose the converse of “If 1  2 , then m1 = m2 .
A. If m1 = m2 , then 1  2
R
1
S
T
2
U
1st Semester Midterm Review
B. If 1  2 , then 2  1
C. If m1 = m2 , then m2 = m1 .
D. None of these
15. Identify the if-then form of the following: All cars have four wheels.
a. If a vehicle has four wheels, then it is a car.
b. If a vehicle is a car, then it has four wheels.
c. If a vehicle is not a car, then it does not have four wheels.
d. None of these
16. The transitive property of equality states “If a = b and b = c, then _____ “.
A. b = a
B. a = c
C. c = b
D. b = b
17. P and Q form a linear pair and mP  62. Find mQ.
A. 62
B. 28
C. 118
D. 90
18. Given l m and m2 = 72, find m3 . ( for 21-23, the rectangle represent parallel lines)
A. 108
C. 18
B. 72
19. Given l m , m1 = 9x +5 and m2 = x + 37, find the value of x.
A. 32
B. 4
C. 41
4
D. 112
D. 39
3
l
1
2
5
m
1st Semester Midterm Review
20. Given m4  5x  2 and m5 = 3x + 28, find the value of x so that l m .
A. 26
B. 13
C. 67
D. 75
21. The measures of two angles of a triangle are 38 and 47. What is the measure of the third angle?
A. 85
B. 95
C. 133
D. 142
22. If IGH  KLJ , then H is congruent to
A. J
B. I
C. K
25. Find the value of x.
26. Find the value of x when a║b.
D. L
1st Semester Midterm Review
27. Solve for x in the diagram.
28. In the diagram, WX ≅ YZ. Find the length of XZ.
29. Find the midpoint and distance of a segment with endpoints A(-8, 5) and B(-2, 7).
30. AB bisects∠CAD. Find the value of x.
31. MQ= 30, MN = 5, MN=NO, and OP=PQ.
Find the length of OQ .
1st Semester Midterm Review
Find QR in the following problems.
1. If RS = 44.6 and SQ = 68.4, find QR.
SQ.
2. If RS = 33.5 and RQ = 80, find
If U is between T and B, find the value of x and the measure of TU . (Hint: Draw
a picture for each problem with the given information and then write the equation to
solve.
22. TU = 2x, UB = 3x + 1,
4x+17,
TB = 21
23. TU = 4x-1, UB = 2x -1,
TB = 5x
Algebraic Proofs: Write a two column proof for the following:
Given: Given: 2(2x+3) - 2 = 3(x-1)
Prove: x = -7
24. TU = 1-x, UB =
TB = -3x
1st Semester Midterm Review
Given: Given: 1/2(2x-4) + 3 = 1/3(3x-9)
Prove: x = 4
1. Angle Bisector
a. A ray that cuts any angle into two congruent halves
b. A ray that cuts any line into two congruent halves
c. A ray that cuts any object into two congruent halves
d. A ray that cuts any segment into two congruent halves
2. Complementary angles
a. Angles whose sum is 180 degrees
b. Angles whose sum is 90 degrees
c. Angles whose sum is 100 degrees
d. Angles whose sum is 0 degrees
3. Supplementary angles
a. Angles whose sum is 90 degrees
b. Angles whose sum is 0 degrees
c. Angles whose sum is 180 degrees
d. Angles whose sum is 100 degrees
4. Vertical angles
a. Two pairs of congruent angles that are formed when two line intersect
b. Four congruent angles that are formed when two line intersect
c. One pair of congruent angles that are formed when two line intersect
d. Exist only in linear pairs
5. Ruler Postulate:
a. Given any two points on a line, the distance cannot be measured
b. Given any two points on a line, the distance can be measured
c. Given any two points on a line, the distance is imaginary
d. Given any two points on a line, there is not distance between them
6. A=B and B=C, then A=C
a. Substitution
1st Semester Midterm Review
b. Segment addition
c. Transitive
d. Reflexive
7. If segment AB = 10m and BC = 5m, then segment AC = 15m
a. Substitution
b. Segment addition
c. Transitive
d. Reflexive
8. If angle A = 15 and angle B = 75, then their measure is:
a. Supplementary
b. Perpendicular
c. Parallel
d. Complementary
9. If a = b, then b = a
a. Transitive
b. Substitution
c. Reflexive
d. Symmetric
Define the following:
1. Definition of Congruence
2. Perpendicular lines
3. Segment Addition Postulate
4. Angle addition Postulate
5. Protractor postulate