Transcript Understanding Geometry Better

A Point
A point is used to indicate a location or position.
We often use a dot ( ●) to mark a point.
●
●
Point A
Point B
●
Point C
Collinear Points
● U
L
O
V
collinear points
E
F
N
noncollinear points
Points that lie on the same line
are called collinear points. If
there is no line on which all of
the points lie, then they are
noncollinear points.
Lines and Line Segments
A line has no endpoints, therefore you
A
line segment
2
cannot
measurehowever,
how longhas
it is.
endpoints and the length of a line
segment can be measured.
Line AB
A
A
B
8cm
B
A Ray
A ray is part of a line. A ray has one
endpoint and go on infinitely in one
direction. A ray cannot be measured
because it only has one endpoint.
B
B
A
Ray AB
Ray BA
A
Curved Lines
A
B
A line can also be curved.
A curved line is called a curve.
Intersecting Lines or Segments
●
Intersecting lines or segments
meet at a point.
Concurrent Lines or Line Segments
●
Concurrent lines or line segments
occur when 3 or more lines meet at
the same point.
Perpendicular Lines or Line Segments
Right angle
When two lines cut to form right
angles (900), we say that the lines are
perpendicular.
Parallel Lines or Line Segments
Two straight lines in a plane are
parallel lines if they do not
intersect .
Skew Lines
Line n
Line m
Skew Lines
Line n
Line m
Skew Lines cannot intersect as
they are not on the same plane
PLANES
Surface of a blackboard
Surface of a mirror
Cover of
a box
Surface of a can
Examples of plane surfaces
A plane may be considered as an
infinite set of points forming a
connected flat surface extending
infinitely far in all directions. A single
capital letter is used to denote a plane.
ANGLES
Here are some examples of angles.
A
Sides
Vertex
B
C
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.
We find everyday life examples that suggest the
idea of an angle.
Naming an angle
.
P●
A ●
B
x
●
W
●
C
Many different names exist for the
same angle. For the angle above,
∠PBC,∠ PBW, ∠CBP, ∠WBA and ∠x
are all names for the same angle.
Measuring Angles
The instrument used to measure
angles is called a protractor . The
unit used is called degree (0)
The measurement of an angle is based
on a circle divided into 360 parts called
degrees(0).
A complete turn ( a full circle) is 3600.
900
00, 3600
1800
2700
Classification of Angles
1. Acute Angles
An acute angle is an angle less than 90 degrees.
630
250
160
850
80
2. Right Angles
A right angle is an angle of exactly 900.
3. Obtuse Angles
An obtuse angle is angle greater than 900 but
less than 1800.
1500
1250
1100
4. Reflex Angles
A reflex angle is an angle greater than 1800 but
less than 3600.
2100
PAIRS OF ANGLES
Complementary Angles
Complementary angles are two angles which
add up to 900. The two angles may or may not
be adjacent.
400
300
600
500
Supplementary Angles
Supplementary angles are two angles whose sum is
1800. The two angles may or may not be adjacent.
1300
500
600
1200
Adjacent Angles
Adjacent angles are two angles lying next to
each other on the same plane with a common
vertex and a common side between them.
C
P
Q
1300
300
A
M
B
500
D
600
R
S
A
H
T
Vertical angles
When two lines intersect each other, the angles
“opposite “ each other are known as vertically
opposite angles.
S
b
P
c
a
d
Q
R
Vertically opposite angles are equal.
∠a = ∠ c
∠b = ∠d
Salamat sa inyong
lahat
Prepared by:
Mrs. Flordelita G. Male
Master Teacher II
San Bartolome High School
Quezon City