Download Geometry Midterm Exam Vocabulary List—January 2012 yy x x d

Geometry Midterm Exam Vocabulary List—January 2012
Most, but not all, of the vocabulary and concepts covered in semester 1 are listed below.
Refer to your class notes and textbooks for additional information.
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Undefined Terms
o Point
o Line
o Plane
Collinear
Noncollinear
Postulate
Theorem
Hypothesis
Conclusion
Conjecture
Counterexample
Conditional Statement
Law of Detachment

Distance Formula

Measure of a straight line = 180°

 x  x2 y1  y2 
Midpoint Formula M  1
,

2 
 2
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
d
 x2  x1 2   y2  y1 2
Perpendicular Bisector
Angle Bisector
Parallel Lines
Angles
o Alternate Interior Angles
o Corresponding Angles
o Vertical Angles
o Same Side Interior Angles
o Supplementary
o Linear Pair
o Complementary
o Congruent
Diagonal
Constructions
o Bisect a segment and angle
o Parallel lines
o Line perpendicular to a given line
 Triangle Congruence Theorems
o AAS-Angle Angle Side
o SSS-Side Side Side
o SAS-Side Angle Side
o ASA-Angle Side Angle
 HL-Hypotenuse Leg
 CPCTC
 Theorem 5 - 8 p258 (see below)
 Median
 Polygons
o Names by number of sides
o Interior angle measures (n – 2)180
o
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Exterior angle measure
360
n
Properties of
o Quadrilaterals
o Squares
o Rhombus
o Parallelograms
o Trapezoids
o Kites
o Rectangles
o Isosceles Triangle
Reflexive Property
Contrapositive
Converse
Negation
Inverse
Truth Tables & Associated Symbols
o ~   
Geometry Midterm Review—January, 2012
____
1. Find a counterexample to show that the conjecture is false.
Conjecture: The product of two positive numbers is greater than the sum of the two numbers.
a.
b.
c.
d.
____
3 and 5
2 and 2
A counterexample exists, but it is not shown above.
There is no counterexample. The conjecture is true.
2. Which statement is the Law of Detachment?
a.
b.
c.
d.
If
If
If
If
is a true statement and q is true, then p is true.
is a true statement and q is true, then
is true.
and
are true, then
is a true statement.
is a true statement and p is true, then q is true.
3. Find the distance between points P(8, 2) and Q(3, 8) to the nearest tenth.
4. The Frostburg-Truth bus travels from Frostburg Mall through the City Center to Sojourner Truth Park. The mall
is 3 miles west and 2 miles south of the City Center. Truth Park is 4 miles east and 5 miles north of the Center.
How far is it from Truth Park to the Mall to the nearest tenth of a mile?
5. Find the coordinates of the midpoint of the segment whose endpoints are H(8, 2) and K(6, 10).
Geometry Midterm Review—January, 2012
Page |1
y
10
6. Find the midpoint of
P
5
–10
–5
5
10 x
–5
Q
–10
7. What is the converse of the following conditional?
If a point is in the first quadrant, then its coordinates are positive.
8. What is the converse and the truth value of the converse of the following conditional?
If an angle is a right angle, then its measure is 90.
9. Use the Law of Detachment to draw a conclusion from the three given statements.
If an elephant weighs more than 2,000 pounds, then it weighs more than Jill’s car.
Smiley the Elephant weighs 2,150 pounds.
10. Find the value of x.
(7x – 8)°
(6x + 11)°
Drawing not to scale
Geometry Midterm Review—January, 2012
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11. Construct the perpendicular bisector of the segment.
12. Construct
the bisector of
____ 13. Line r is parallel to line t. Find m 5. The diagram is not to scale.
r
7
135°
1
t
a. 45
3
4
2
5
6
b. 35
Geometry Midterm Review—January, 2012
c. 135
d. 145
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This diagram of airport runway intersections shows two parallel runways. A taxiway crosses both
runways.
____ 14. If 8 measures 119, what is the sum of the measures of 1 and 4?
a. 122
b. 238
c. 119
____ 15. How are
and
related?
a. corresponding angles
b. alternate interior angles
d. 299
c. same-side interior angles
d. none of these
____ 16. Complete this statement. The sum of the measures of the exterior angles of an n-gon, one at each vertex, is ____.
a. (n – 2)180
b. 360
c.
d. 180n
____ 17. Complete this statement. A polygon whose sides all have the same length is said to be ____.
a. regular
b. equilateral
c. equiangular
d. Convex
____ 18. Find
. The diagram is not to scale.
98°
96°
116°
118°
100°
104°
115°
120°
A
Geometry Midterm Review—January, 2012
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____ 19. A nonregular hexagon has five exterior angle measures of 55, 60, 69, 57, and 57. What is the measure of the
interior angle adjacent to the sixth exterior angle?
a. 128
b. 118
c. 62
d. 108
____ 20. Which two statements contradict each other?
I. Jon, Elizabeth, and Franco read 27 books among them for a class.
II. Franco read 6 books.
III. None of the three students read more than 7 books.
a. I and II
b. I and III
c. II and III
d. No two of the statements contradict each other.
____ 21. Which statement is true?
a. All quadrilaterals are rectangles.
b. All quadrilaterals are squares.
c. All rectangles are quadrilaterals.
d. All quadrilaterals are parallelograms.
_____ 22. Which of the following additional pieces of information is needed in order to prove that ABC  DEF?
A
A  D
B
AC  DF
C
AB  EF
D
A  F
A
B
D
C
E
F
23. Classify the figure in as many ways as possible.
Geometry Midterm Review—January, 2012
Page |5
24. What guarantees a quadrilateral is a rectangle?
25. Justify the last two steps of the proof.
Given:
and
Prove:
M
Proof:
1.
N
O
1. Given
2. Given
3.
4.
2.
3.
4.
P
26. What other information do you need in order to prove the triangles congruent
A
using the SAS Congruence Postulate?
B
C
27. In ΔAEC, G is the centroid and BE = 9. Find BG and GE.
C
B
A
Geometry Midterm Review—January, 2012
D
G
F
D
E
Page |6
28. What is the contrapositive of this statement?
If a figure has three sides, it is a triangle.
29. What is the negation of this statement?
The angle is not obtuse.
30.
Write the converse of the following statement. Is the converse true or false?
If the name of an angle is ABC, then the vertex of the angle is B.
31.
Construct a line perpendicular to
the given line l through the given point K.
K
l
32. Name the line and plane shown in the diagram.
T
U
S
R
33. Name the intersection of plane BPQ and plane CPQ.
34. Based on the information in the diagram, can you prove that the figure is a
parallelogram? Explain.
Geometry Midterm Review—January, 2012
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35. Given:
and
. Find the length of AB
B
D
2x + 10
C
4x -20
A
E
36. Complete the truth table.
p
q
T
T
T
F
F
T
F
F
~p
~q
pq
pq
pq
37. Write the first step needed to prove the following statement:
“If a triangle is acute then all three angles measure less than 90°”
a.
b.
c.
d.
A triangle is an acute triangle
A triangle is not an acute triangle
A triangle has all three angles less than 90°
The sum of measures of the interior angles of a triangle is 180°
From the textbook:
pg
pg
pg
pg
pg
pg
pg
pg
pg
79
91
131
132
146
147
165
168
201
#27-31
#1
Investigation
proof of 3-7
Check for understanding #4
#16
Check for understanding #1
#1
#8
Geometry Midterm Review—January, 2012
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