This document defines and describes basic geometric shapes and concepts including points, lines, rays, segments, angles, circles, polygons, triangles, quadrilaterals, symmetry, and more. Key points covered are: - A point has no size or parts, a line has infinite length but no width, a ray has a starting point and extends infinitely in one direction, and a segment is a portion of a line with fixed length between two points. - Angles are measured by the distance between intersecting lines, and can be acute, right, obtuse, straight, or reflex. Adjacent angles and complementary/supplementary angle pairs are also defined. - Circles are sets of points equidistant from

1. MODERN GEOMETRY Section 2.1
Thompson

2. A
POINT
“That which has no part”
• Has no size
• Denoted by capital
letter
• Location on plane

3. A D
LINE
“Breadthless length”
• Has no width
• Infinite length of
“connected” points
• Represented with two
arrows
• Say: “Line AD”
• Write: AD
• Each line contains at least two distinct points
• Any two points contain one and only one
line
• Points that lie on the same line are said to
be collinear

4. A
B
D
G
RAY
“Breadthless length”
• Has no width
• Infinite length of “connected”
points, with starting point
• Represented with one arrow
• Say: “Ray GB”
• Write:
• Starting point matters
GB

5. A
B C
D
G
SEGMENT
“Breadthless length”
• Has no width
• Fixed length of “connected”
points, with starting/ending
point
• Represented with no arrows
• Say: “Segment GC”
• Write: GC

6. ANGLES
“measure of distance”
• Lines meeting at a common
endpoint
• We call this sides and vertex
(pl. vertices)
• Need three points to name
• Say: “Angle AGB or Angle
BGA”
• Write: BGAorAGB 
A
B C
D
G
*Vertex is the middle point
GABAGB 

7. ANGLES
Protractor Postulate
• Basically “we’re allowed
to measure angles with a
protractor”
• We’ll start with degrees
• Line up one side with 0°
or 180 °
• So, m∠𝐴𝐺𝐵= 77°
A
B C
D
G

8. ANGLES
Types of Angles
• Right – 90°
• Perpendicular
• Write: 𝐺𝐶 ⊥ 𝐺𝐸
• Acute – between 0° and 90°
• Obtuse – between 90° and 180°
• Straight – 180°
• Reflex – between 180° and 360°
A
B C
D
G
E
54°

9. ANGLES
Congruent Angles
• Have the same measure
• Say: “angle BGC is
congruent to angle AGF”
• Write:
• Notate using “little arcs”
A
B C
D
G
E
54°
AGFBGC 
F

10. ANGLES
Adjacent Angles
• Share common side and
vertex
• Say: “angle BGC is
adjacent to angle CGD”
A
B C
D
G
E
54°
F

11. ANGLES
Angle Addition Postulate
• Smaller adjacent angles
must sum to the whole
angle
• Can find unknown angles
by setting up algebra
equations
• Find m∠DGE, etc.
A
B C
D
G
E
54°
F
77°

12. ANGLES
Angle Pairs
• Complementary – Angles
whose measures sum to 90°
• Supplementary – Angles
whose measures sum to 180°
A
B C
D
G
E
54°
F
77°

13. CIRCLES
The set of all points equidistant
from a given point
• Center point
• Say: “Circle C”
• Radius = ½ Diameter
• Chord
• Tangent
C
r
D
E
F
A
B

14. POLYGONS
A simple, closed curve of line
segments
• Named by its vertices
• Have adjacent sides, and
adjacent angles
• Congruent sides marked with
hash mark(s)
A
B
C
E D

15. POLYGONS
Type of Polygon / # sides
• Triangle 3
• Quadrilateral 4
• Pentagon 5
• Hexagon 6
• Octogon 8
• Decagon 10
• n – gon n

16. POLYGONS
Regular Polygon
• All sides and angles are
congruent

17. TRIANGLES
Characterized by sides or angles
• Write as ΔABC
• Interior angle sum
• ∠A + ∠B + ∠C = 180°
A
B C

18. TRIANGLES
Classifying…
• By Sides
• By Angles

19. QUADRILATERALS
Characterized by their sides,
angles, and parallel lines
• Parallel lines are in the same
plane and do not intersect
• Parallel lines can be marked
with “arrows”

20. QUADRILATERALS
SQUARE
All sides congruent, all angles
are right.

21. QUADRILATERALS
RECTANGLES
All angles are right.

22. QUADRILATERALS
RHOMBUS
All sides are congruent

23. QUADRILATERALS
PARALLELOGRAM
Opposite sides are parallel

24. QUADRILATERALS
TRAPEZOID
Exactly on pair of sides is
parallel

25. QUADRILATERALS
KITE
Two pairs of adjacent and
congruent sides

26. QUADRILATERALS

27. SYMMETRY
Reflection Symmetry
• An imaginary line such that
the figure can be folded
exactly unto itself

28. SYMMETRY
Rotational Symmetry
• If shape is identical even if
turned less than full rotation

29. CLASSWORK / HOMEWORK
Worksheet
Check BlackBoard
Get Textbook / Supplies
Read Chapter 2