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Chapter 2
Introducing Geometry
Lesson 2.1
• Definition – a statement that clarifies or
explains the meaning of a word or a
phrase.
• Point – an undefined term. The basic unit
of geometry. It has no size, is infinitely
small, and has only location. Named with a
capital letter.
• Line – an undefined term. A straight
arrangement of points. There are infinitely
many points in a line. A line has infinite
length but no thickness and extends
forever in two directions. Named with two
capital letters representing points and a
line over.
M
N
• Plane – an undefined term. A plane has
length and width but no thickness. It is a
flat surface that extends forever.
• Collinear points – two or more points that
lie on the same line or segment.
D
C
E
Coplanar points – two or more points
that lie on the same plane.
F
H
G
• Space – the set of all points.
Line segment – two points and all the points
between them that lie on the line
containing the two points. The two points
are called the endpoints of the line
segment.
I
J
• Ray – ray AB is the part of the line AB that
contains point A and all the points on line
AB that are the same side of point A as
point B. A is the endpoint.
A
B
• Angle – two rays that share a common
endpoint provided the two rays do not lie on
the same line.
R
S
T
Vertex – the corner of the angle. In this picture it
is S.
Lesson 2.2
• Congruent – two geometric figures are
congruent if and only if they are identical in
shape and size. 
U
X
V
W
Y
B1
Z
A1
Lesson 2.3
• Conditional statement – a statement that
can be expressed as an if-then statement.
For example “If a polygon is a hexagon,
then it has exactly six sides.”
• Converse – the statement formed by
reversing the two parts of a conditional
statement. For example “If a polygon has
exactly six sides, then it is a hexagon.”
Biconditional statement – a statement in
which a conditional statement and its
converse are both true and are combined
into one statement. “A polygon is hexagon
if and only if it has exactly six sides.”
Counterexample – an example that proves a
statement wrong.
• Right angle – an angle whose measure is
90 degrees.
B
C
A
• Acute angle – an angle whose measure is
less than 90 degrees.
B
A
C
D
E
F
• Obtuse angle – an angle whose measure
is greater than 90 degrees.
A
C
B
D
E
F
• Midpoint of a segment – the middle of the
segment such that it divides the original
segment in half.
A
C
B
• Angle bisector – a ray that has an
endpoint on the vertex of an angle and
that divides the angle into two angles of
equal measure.
A
B
C
Lesson 2.4
• Parallel lines – two or more lines that lie in the
same plane and that do not intersect.
• Skew lines – lines that are not in the same
plane and do not intersect.
• An example of this would be a pencil
through a piece of paper.
• Perpendicular lines – two lines that intersect to
form a right angle. 
• Complementary angles – two angles
whose measure have the sum of 90
degrees.
mABC = 30.20
mDEF = 59.75
C
A
E
D
B
F
• Supplementary angles – two angles
whose measure have the sum of 180
degrees.
mHIG = 126.38
mJKL = 53.79
G
H
I
K
J
L
• Vertical angles – two lines intersect and
the angles that are across from each
other.
N
M
Q
O
P
• Linear pair of angles – two angles that
form a line.
T
R
S
U
Lesson 2.5
• Polygon – a closed geometric figure in a
plane in which line segments connect
endpoint to endpoint and each segment
intersect exactly two others.
• Convex polygons
• Concave polygons
Classify polygons
Sides
Name
Sides Name
Sides Names
3 Triangles
7 Heptagon
11 undecagon
4 Quadrilateral
8 Octagon
12 Dodecagon
5 Pentagon
9 Nonagon
6 Hexagon
10 Decagon
N
n-gon
• Consecutive – they are right next to each
other.
• Perimeter – the sum of the lengths of all
the sides.
• Diagonal of a polygon – a segment
connecting any two nonconsecutive
vertices.
• Equilateral polygon – a polygon whose
sides are equal in measure.
• Equiangular polygon – a polygon whose
angles are equal in measure.
• Regular polygon – a polygon that is both
equilateral and equiangular.
Lesson 2.6
• Right Triangle – a triangle with exactly one
right angle.
• Acute triangle – a triangle with three acute
angles.
• Obtuse triangle – a triangle with exactly
one obtuse angle
• Scalene triangle – a triangle with three
sides of different lengths.
• Isosceles triangle – a triangle with at least
two sides the same length.
• Equilateral triangle – a triangle with all
sides equal.
• Median of a triangle – a segment
connecting the midpoint of a side to the
opposite vertex.
V
Z
X
A1
Y
W
• Altitude of a triangle – a perpendicular
segment from a vertex to the opposite side
of the line containing the opposite side.
V
X
B1
W
Lesson 2.7
• Trapezoid – a quadrilateral with exactly
one pair of parallel sides.
A
D
B
C
• Kite – a quadrilateral with exactly two pairs
of distinct congruent consecutive sides.
• Parallelogram – a quadrilateral in which
both pairs of opposite sides are parallel.
• Rhombus – an equilateral parallelogram.
• Rectangle – an equiangular parallelogram
• Square – an equiangular rhombus and
equilateral rectangle.
Lesson 2.9
• Locus of points – the set of all points in a
plane that satisfy some given condition or
property.