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Geometry
First Semester Exam
Part I: Vocabulary
acute angle
acute triangle
adjacent angles
alternate exterior angles
alternate interior angles
altitude
angle
angle bisector
base angles
betweeness
centroid
circumcenter
collinear
complementary
compound statement
concave
concurrent lines
conditional statement
congruence transformations
congruent
congruent triangles
conjecture
conjunction
consecutive interior angles
construction
contradiction
convex
coordinate proof
coplanar
corollary
corresponding angles
corresponding angles postulate
counterexample
cross products
deductive argument
deductive reasoning
degree
disjunction
distance
equiangular triangle
equidistant
equilateral triangle
exterior
exterior angle
Name __________________________________hr __
Date ____/____/____ Score:
flow proof
formal proof
if –then statement
incenter
included angle
included side
indirect proof
indirect reasoning
inductive reasoning
informal proof
interior
interior angles
isosceles triangle
line
line segment
linear pair
logically equivalent
means
median
midpoint
midsegment
negation
n-gon
non-Euclidean geometry
obtuse angle
obtuse triangle
opposite rays
orthocenter
paragraph proof
parallel lines
parallel planes
perimeter
perpendicular
perpendicular bisector
plane
plane Euclidean geometry
point
point concurrency
point-slope form
polygon
precision
proof
proof by contradiction
proportion
ratio
rate of change
regular polygon
related conditionals
remote interior angles
right angle
right triangle
scale factor
scalene triangle
segment bisector
sides
similar polygons
skew lines
slope
slope-intercept form
space
spherical geometry
statement
supplementary
transversal
truth table
truth value
two-column proof
undefined terms
vertex
vertex angle
vertical angles
Choose from the terms above to complete each sentence.
1. Two lines are ____________________________ if they intersect to form a right angle.
2. Two angles are____________________________ if their measures have a sum of 90°.
3. When two rays intersect with a common endpoint a(n) ____________________________ is formed.
4. The____________________________ is the point located halfway between the endpoints of a segment.
5. ____________________________are nonadjacent angles formed by the intersection of two lines.
6. A(n) ____________________________ divides an angle into two congruent angles.
7. Two angles are____________________________ if their measures have a sum of 180°.
8. Two angles that lie in the same plane are called____________________________ if they share a common
side and a common vertex.
9. A(n) ____________________________ is an angle whose measure is less than 90°.
10. Two segments are ____________________________if they have the same measure.
11. A false example is called a ____________________________.
12. A ____________________________is an educated guess based on known information.
13. ____________________________uses facts, rules, definitions, or properties to reach logical conclusions.
14. 4 and 5 are ____________________________ .
15. According to the____________________________ , line r
is parallel to line t given 3  8.
16. Given r
t, then ____________________________ 4 and 6 are supplementary.
17. Line p is a _____________________ since it intersects or more lines in a plane at different points.
18. When a linear equation is written in the form y = mx + b, m is the ____________________________of the
line and b is the y-intercept.
19. ____________________________ are located between the lines cut by a transversal.
20. If two lines do not intersect and are everywhere equidistant, the lines
are____________________________ .
21. The Perpendicular Transversal Theorem states that in plane, if a line is perpendicular to one of two parallel
lines,
then it is____________________________ to the other.
22. The ratio of the rise to the run of a line is called its ____________________________.
23. A triangle that is equilateral is also called a(n) ____________________________ .
24. A(n) ____________________________has at least one obtuse angle.
25. The sum of the ____________________________is equivalent to the exterior angle of a triangle.
26. The ____________________________angles of an isosceles triangle are congruent.
27. A triangle with different measures for each side is classified as a(n) ____________________________ .
28. A ____________________________organizes a series of statements in logical order written in boxes and
uses arrows to indicate the order of the statements.
29. A triangle that is translated, reflected or rotated and preserves its shape, is said to be a(n) _____________ .
30. The ASA postulate involves two corresponding angles and their corresponding______________________.
31. A ____________________________uses figures in the coordinate plane and algebra to prove geometric
concepts.
32. The ____________________________is formed by the congruent legs of an isosceles triangle.
33. The ____________________________of a triangle is a segment whose endpoints are a vertex of a triangle
and the midpoint of the side opposite the vertex.
34. The ____________________________of a triangle is the point where the altitudes of the triangle intersect.
35. The point of concurrency of the perpendicular bisectors of a triangle is called the ____________________.
36. The____________________________ of a triangle is the intersection of the medians of the triangle.
37. ____________________________can be used to prove statements in geometry and prove theorems.
38. The _________________________ of a triangle is the intersection of the angle bisectors of the triangle.
39. The ____________________________of a triangle is a line, segment, or ray that passes through the
midpoint of a side and is perpendicular to that side.
40. The____________________________ is the point where three or more lines intersect.
41. An indirect proof is a proof where you assume that the conclusion is false and then show that this
assumption leads to a __________________of the hypothesis, a definition, postulate, theorem, or some other
accepted fact.
42. If there are 15 girls and 9 boys in an art class, the ____________________________of girls to boys in the
class is 5:3.
43. If ABC ~ DEF, AB = 10, and DE = 2.5, then the ____________________________of ABC to DEF
is 4:1.
44. In LMN, P lies on LM and Q on LN. If PQ = ½MN, PQ is called a(n) ____________________________.
45. If quadrilaterals ABCD and WXYZ have corresponding angles congruent and corresponding sides
proportional, they are called ____________________________.
46. The equation
3 24

is called a(n) __________________________________.
x 30
47. The ___________________________ of the product of the equation
3 24

are 24x and 90.
x 30
Part II: Proofs
Complete each of the following.
Find the measure of each angle.
a = __________
b = __________
c = __________
d = __________
e = __________
f = __________
g = __________
h = __________
2 – 5 COMPLETE FOUR OF THE FOLLOWING PROOFS.
B. Given: DF  AB
A. Given: 2x – 7 = 14 – x
Prove: x = 7
E
F
A
B
Prove: AB = DE + EF
__________________________________________
C. Given: 1 & 2 are Right Angles
Prove: 1  2
D
2
1
(Do not use: All right angles congruent.)
__________________________________________
__________________________________________
D. Given: 1  8
Prove: a b
(Do not use: Alt exterior angles
Congruent form parallel lines)
__________________________________________
F. Given: PQ SR , PQ  SR
E. Given: L is the midpoint of WE
R
WR ED
Prove: WR  ED W
E
L
__________________________________________
D
Prove: SP  QR
__________________________________________
G. Given: 1  2
1
Prove: a b
a
(Do an indirect proof)
2
b