7. Basics of Geometry
•
•
Extend in two direction
Represented with straight line with two arrowheads to
indicate that the line extends without end in two directions.
Line
B
l
A
This is Line l, (using the lower case
script letter) or symbolically we call it A B
NOTICE: The arrowheads are in
both directions on the symbol AB
11. Basics of Geometry
Plane
• Extend in four direction .
• Represented by a slanted 4 sided figure, but you
must envision it extends without end, even
though the representation has edges.
A
B C
M This is Plane M or plane ABC (be
sure to only use three of the
points when naming a plane)
19. Basics of Geometry
Ray
Symbolized by A B
The initial point is
always the first
letter in naming a
ray. Notice the
difference in
symbols from both
a line and segment.
A B
A is called the initial
point
Ray AB extends in
one direction
without end.
Let’s look at a ray:
21. Basics of Geometry
Not all symbols are created equal!
Symbol alert!
AB is the same as BA
AB BA
is the same as
BUT…
A B
A B
22. Basics of Geometry
AB is not the same as BA
Symbol alert!!
A B AB
A B BA
Initial point 1st
The ray is different!
Notice that the initial point is listed first in the symbol. Also
note that the symbolic ray always has the arrowhead on the right
regardless of the direction of the ray.
23. Basics of Geometry
Opposite Rays
If C is between A and B,
A C B
then CA and CB are opposite rays.
C is the common initial point for the
rays!
24. Basics
Geome
Rays are important because they help us define something very
important in geometry…Angles!
An angle consists of two different rays that have the same initial
point. The rays are sides of the angles. The initial point is called the
vertex.
Angles
Notation: We denote an angle with
three points and symbol. The
middle point is always the vertex.
We can also name the angle with
just the vertex point. This angle can
be denoted as:
BAC,CAB,or A
vertex
sides
A
B
C
25. Basics of Geometry
Classifying Angles
Angles are classified as acute, right, obtuse, and straight,
according to their measures. Angles have measures greater
than 0° and less or equal to 180°.
A
Acute angle
0°< m A < 90°
A
Right angle
m A = 90°
A
Obtuse angle
90°< m A < 180°
A
Straight angle
m A = 180°
27. You will learn to classify
angles as acute,
obtuse, right, or
straight.
28. What is an angle?
Two rays that share the same endpoint form an angle. The
point where the rays intersect is called the vertex of the
angle. The two rays are called the sides of the angle.
30. We can identify an angle by using a point on
each ray and the vertex. The angle below
may be identified as angle ABC or as angle
CBA; you may also see this written as
ABC or as CBA. The vertex point is
always in the middle.
31. Angle Measurements
We measure the size of an angle using
degrees.
Here are some examples of angles and
their degree measurements.
32. Acute Angles
An acute angle is an angle measuring
between 0 and 90 degrees.
The following angles are all acute angles.
33. Obtuse Angles
An obtuse angle is an angle measuring
between 90 and 180 degrees.
The following angles are all obtuse.
34. Right Angles
A right angle is an angle measuring 90
degrees.
The following angles are both right angles.
36. GAME TIME!
The object of the game is to be the first to
raise your hand and correctly name what
type of angle you see.
The correct answer will be on the following slide!!
Good luck!
57. Quadrilateral ……………………… It is a
figure which has four sides
Parallelogram …………………. It has four
side and opposite sides are parallel.
Parallelogram is a quadrilateral with
opposite sides parallel.
58. Rectangle
It has four sides
Opposite sides would be parallel and equal
All angles should be of 90o
Rectangle is basically a parallelogram with
all angles of 90o
All rectangles are quadrilateral but all
quadrilateral are not rectangle
59. Square
Four equal sides
All angles should be of 90o
is a square a rectangle ? Yes/no?
Is a square a quadrilateral? (yes/no)
Is a rectangle a square? Yes/no
60. Quadrilaterals
But only those quadrilateral which has opposite sides
parallel are called
And only those parallelogram are called rectangle in which
angle is 90
And only those rectangles are square in which all side are
61. A square is also a
Rectangle
Parallelogram
Quadrilateral
