Geometry Cheat Sheet
Geometric Terms
Term
Point
Illustration/Notation
Definition
An exact location
use a capital letter
A straight path going
in opposite directions
with no endpoints
Line
use 2 capital letters
⃡ 𝑜𝑟 𝑄𝑃
⃡
line 𝑃𝑄
A straight path going
in one direction from
one endpoint
Ray
use 2 capital letters; the endpoint and any other point
on the ray
ray 𝑃𝑄; NOT ray 𝑄𝑃
Line
Segment
use 2 capital letters
̅̅̅̅ and 𝑄𝑃
̅̅̅̅ are different names for the same line
𝑃𝑄
segment
Congruent
Similar
Part of a line
containing two
endpoints and all the
points between the
endpoints
≅
The same measure
~
Same shape, not necessarily
same size
Types of Lines
Parallel lines – lines that will never
Perpendicular lines – lines that intersect
Intersecting lines – lines
intersect
to form right angles
that cross and form two sets of
vertical angles that are equal &
opposite each other
a
a
b
b
a ∥ b – line a is parallel to line b
a ⊥b – line a is perpendicular to line b
Angles
Angle – two rays that share a common endpoint called the vertex
 angles are measured in degrees
 angles are named by their vertex, by their points, or by an angle number.
𝑻𝒉𝒊𝒔 𝒂𝒏𝒈𝒍𝒆 𝒄𝒂𝒏 𝒃𝒆 𝒏𝒂𝒎𝒆𝒅 𝒕𝒉𝒆 𝒇𝒐𝒍𝒍𝒐𝒘𝒊𝒏𝒈 𝒘𝒂𝒚𝒔 ∠𝑨𝑩𝑪, ∠𝑩, or ∠𝟒
*the "∠" symbol represents an angle
Types of angles
straight – Exactly 180°
acute – less than 90°
right – exactly 90°
adjacent – angles that share
a common side
complementary – angles
that add up to 90°
supplementary – angles reflex – greater than 180°
that add up to 180°
obtuse – greater than 90°
Polygons
Polygon – a closed, plane figure with sides that are line segments
Polygon
Number of Sides and Vertices
Regular polygon – ALL SIDES and ALL ANGLES are
Triangle
3
congruent.
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
4
5
6
7
8
9
10
Picture must indicate congruent
sides and angles by ‘tick marks’
angle congruency mark.
•Interior angles – the sum of the interior angles of a polygon, where n = # of sides, is: 180(n – 2)
•Diagonals – the number of diagonals in a polygon, where n = # of sides, is: n(n – 3)
2
Triangles – a closed figure with three sides. All angles add up to 180°. The sum of the lengths of any two sides
has to be greater than the 3rd side. (Ex. Side lengths of 3, 10 & 7 could not form a triangle because 7+3 is not > 10).
Types of triangles (based on angle measures)
Acute – all acute angles
Right – ONE right angle
Obtuse – ONE obtuse angle
Types of triangles (based on sides)
Scalene – no sides congruent
-no angles congruent
Equilateral – all sides &
angles are congruent
Isosceles – two sides congruent
-two angles congruent
The two “tick
marks” show that
those sides are the
same length
Quadrilaterals - a closed figure with four sides. All angles add up to 360°
“tick marks” show that
all the sides are the
same length; three
marks on the angles
show they are the same
size
Properties of Circles
Radius (r) – distance from the edge to the center.
Chord – a line segment whose endpoints are both on a circle.
Diameter (d) – any chord that passes through the center of a circle (Note: d = 2r)
Circumference (c) – the perimeter of a circle ( c = dπ or c = 2rπ )
Pi (π) – the ratio of the circumference to the diameter of a circle; approximately 3.14 or 22/7
Area = πr2
Properties of Right Triangles
Pythagorean Theorem: a2 + b2 = c2
Legs (a & b) – sides that form the right angle.
Hypotenuse (c) – side opposite the right angle (the longest side)
Properties of Parallel Lines Cut by a Transversal
Given: EF ║ GH :

Eight sets of supplemental angles; Ex.

Several sets of congruent angles that include:
o Vertical angles; Ex.
o Corresponding angles (same relative position); Ex.
o Alternate interior angles - inside ║lines and on opposite sides of transversal; Ex.
o Alternate exterior angles – outside the ║lines and on opposite sides of the transversal; Ex.