Download Unit 1 Review KEY - Ector County ISD.

Name:______________________________ Period:_______ Date:__________________
Unit 1 Review KEY
I.
Terminology: Match the following terms with their definitions.
1.
Euclidean Geometry
2.
Undefined Term
3.
Point
4.
Line
j
5.
Plane
v
6.
Defined Term
o
7.
Parallel Lines
u
8.
Perpendicular Lines
9.
Skew Lines
a.
x
t
s
n
10. Line Segment
11. Ray
12. Proof
w
y
z
q
13. Theorem
r
14. Conjecture
k
15. Inductive Reasoning
l
16. Deductive Reasoning
m
17. Conditional Statement
g
18. Direct Reasoning
h
19. Converse Statement
i
20. Inverse Statement
d
21. Contrapositive Statement
22. Biconditional Statement
23. Corollary
a
24. Counterexample
25. Definition
c
26. Postulate
p
b
e
f
A theorem whose proof follows directly from another
theorem.
b. An example that proves that a conjecture or statement is
false.
c. A statement that describes a mathematical object and can be
written as a true biconditional statement.
d. The statement formed by negating the hypothesis and
conclusion of a conditional statement.
e. The statement formed by both exchanging and negating the
hypothesis and conclusion of a conditional statement.
f. A statement that can be written in the form “p if and only if
q.”
g. A statement that can be written the form “if p, then q”,
where p is the hypothesis and q is the conclusion.
h. The process of reasoning that begins with a true hypothesis
and builds a logical argument to show that a conclusion is
true.
i. The statement formed by exchanging the hypothesis and
conclusion of a conditional statement.
j. An undefined term in Geometry, it is a straight path that has
no thickness and extends forever.
k. A statement that is believed to be true.
l. The process of reasoning that a rule or statement is true
because specific cases are true.
m. The process of using logic to draw conclusions.
n. Lines that are not coplanar.
o. A figure that is defined in terms of undefined terms and
other figures.
p. A statement that is accepted as true without proof. Also
called an axiom.
q. An argument that uses logic to show that a conclusion is
true.
r. A statement that has been proven.
s. Lines that intersect at 90 angles.
t. An undefined term Geometry, it names a location and has
no size.
u. Lines in the same plane that do not intersect.
v. An undefined term in Geometry, it is a flat surface that has
no thickness and extends forever.
w. The system of geometry described by Euclid.
x. A basic figure that is not defined in terms of other figures.
The figures are point, line, and plane.
y. A part of a line consisting of two end points and all points
between them.
z. A part of a line that starts at an endpoint and extends
forever in one direction.
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II.
Segment Length:
Distance Formula:
Midpoint Formula:
𝑥1 + 𝑥2
(
,
2
𝑑 = √(𝑥1 − 𝑥2 )2 + (𝑦1 − 𝑦2 )2
Calculate the distance and midpoint between following sets of points.
1. A(5, 8) and B(-3, 6)
𝑑 = √(5 − −3)2 + (8 − 6)2
5+−3
(
2
8+6
,
)
2
(1, 7)
𝑑 = 8.25
2. C(5, -9) and D(-11, 7)
𝑑 = √(5 − −11)2 + (−9 − 7)2
(
5+−11
2
−9+7
,
2
(−3, −1)
𝑑 = 22.63
3. G(4, 7) and H(-1, -5)
𝑑 = √(4 − −1)2 + (7 − −5)2
4+−1
(
2
,
7+−5
2
)
3
𝑑 = 13
(2 , 1)
4. K(-2, -5) and L(5, 8)
𝑑 = √(−2 − 5)2 + (−5 − 8)2
𝑑 = 14.76
−2+5
(
2
,
3
−5+8
2
3
(2 , 2)
Calculate the indicated length:
5. Find NQ.
NQ = 4 + 17 = 21
6. Find ST.
ST = 37 – 18 = 19
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)
)
𝑦1 + 𝑦2
)
2
Use the number line to find the indicated distance.
7. LM = 6
8. JL = 9
9. JM = 16
III.
Angle Measures: Use the following diagram:
1. supplement of AEB 180° – 50° = 130°
2. complement of AEB 90° – 50° = 40°
3. x  _________________________
x + 15 = 50
-15
-15
x = 35
4. y  ________________________
50 + y + 30 = 180
y + 80 = 180
-80
-80
y = 100
5. mDEC  °
6. mAED  180 – 50 = 130°
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IV.
Conditionals: Rewrite the following conditional statements into the converse,
inverse and contrapositive forms. Them determine the validity of each statement.
If it is false, provide a counterexample.
1. If two angles are adjacent, then they share a common side.
Converse:
Inverse:
Statement:
If two angles share a common side, then they
are adjacent.
Validity:
TRUE
If two angles are not adjacent, then they do
not share a common side.
TRUE
Contropositive: If two angles do not share a common side,
then they are not adjacent.
TRUE
2. If two angles are vertical, then they are congruent.
Converse:
Inverse:
Statement:
If two angles are congruent, then they are
vertical angles.
If two angles are not vertical, then they are
not congruent.
Contropositive: If two angles are not congruent, then they are
not vertical.
V.
Validity:
FALSE, two
adjacent
congruent
angles.
FALSE, two
non-vertical
right angles are
congruent.
TRUE
Other: Review your Cornell Notes on Notetaking
Turn in your complete reviews and Cornell Notes on
Notetaking for some extra points.
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