Proof Geometry
Name __________________________________hr __
First Semester Exam Review
Part I: Vocabulary
Date ____/____/____ Score:
Choose from the terms at the end of this worksheet to complete each sentence.
1. Two lines are perpendicular if they intersect to form a right angle.
2. Two angles are complementary if their measures have a sum of 90°.
3. When two rays intersect with a common endpoint a(n) angle is formed.
4. The midpoint is the point located halfway between the endpoints of a segment.
5. Vertical angles are nonadjacent angles formed by the intersection of two lines.
6. A(n) angle bisector divides an angle into two congruent angles.
7. Two angles are supplementary if their measures have a sum of 180°.
8. Two angles that lie in the same plane are called adjacent if they share a common side and a common
vertex.
9. A(n) acute angle is an angle whose measure is less than 90°.
10. Two segments are congruent if they have the same measure.
11. A false example is called a counterexample.
12. A conjecture is an educated guess based on known information.
13. Deductive reasoning uses facts, rules, definitions, or properties to reach logical conclusions.
14. 4 and 5 are alternate interior angles .
15. According to the corresponding angles postulate , line r
is parallel to line t given 3  8.
16. Given r || t, then consecutive interior/ same side interior angles 4 and 6 are supplementary.
17. Line p is a transversal 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 slope of the line and b is the y-intercept.
19. Interior angles are located between the lines cut by a transversal.
20. If two lines do not intersect and are everywhere equidistant, the lines are parallel .
21. The Perpendicular Transversal Theorem states that in plane, if a line is perpendicular to one of two parallel
lines, then it is perpendicular to the other.
22. The ratio of the rise to the run of a line is called its slope or rate of change.
23. A triangle that is equilateral is also called a(n) equiangular triangle .
24. A(n) obtuse triangle has at least one obtuse angle.
25. The sum of the remote interior angles is equivalent to the exterior angle of a triangle.
26. The base angles angles of an isosceles triangle are congruent.
27. A triangle with different measures for each side is classified as a(n) scalene triangle.
28. A flow proof 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) congruence
transformation .
30. The ASA postulate involves two corresponding angles and their corresponding included sides.
31. A coordinate proof uses figures in the coordinate plane and algebra to prove geometric concepts.
32. The vertex angle is formed by the congruent legs of an isosceles triangle.
33. The median 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 orthocenter 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 circumcenter.
36. The centroid of a triangle is the intersection of the medians of the triangle.
37. Indirect reasoning can be used to prove statements in geometry and prove theorems.
38. The incenter of a triangle is the intersection of the angle bisectors of the triangle.
39. The perpendicular bisector 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 point of concurrency 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 contradiction 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 ratio of girls to boys in the class is 5:3.
43. If ABC ~ DEF, AB = 10, and DE = 2.5, then the scale factor 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) midsegment.
45. If quadrilaterals ABCD and WXYZ have corresponding angles congruent and corresponding sides
proportional, they are called similar polygons.
46. The equation
3 24

is called a(n) proportion.
x 30
47. The cross products of the product of the equation
3 24

are 24x and 90.
x 30
Part II: Proofs
Complete each of the following.
𝑷𝑸 ≅ 𝑺𝑹
Given
𝑹𝑺𝑸  𝑷𝑸𝑺
Alternate Interior Angles
 when lines are parallel.
∆𝑹𝑺𝑸
SAS
CPCTC
𝑺𝑸
Same side or
Reflexive property
AAS
Vertical Angles 
CPCTC
SAS
Vertical Angles 
Find the measure of each angle.
a = 22
b = 22_
c = 79
d = 79
e = 136
f = 12
g = 78
h = 80
CPCTC
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
Word Bank
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
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