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THE CLERMONT SCHOOL
GEOMETRY RELEARNING WORKSHOP
SEVENTH
BASIC CONCEPTS OF GEOMETRY
Line segments
Points
A line segment connects two endpoints. A line segment
̅̅̅̅
with two endpoints A and B is denoted by 𝐴𝐵
We may think of a point as a "dot" on a piece of paper
or the pinpoint on a board. In geometry we usually
identify this point with a number or letter. A point has
no length, width, or height - it just specifies an exact
location. It is zero-dimensional.
Rays
A ray starts from one endpoint and extends forever in
one direction. 𝐴𝐵
Planes
Lines
A line is one-dimensional. That is, a line has length, but
no width or height. In geometry, a line extends forever
in both directions. A line is uniquely determined by two
points.
Planes are two-dimensional. A plane has length and
width, but no height, and extends infinitely on all sides.
Planes are thought of as flat surfaces, like a tabletop. A
plane is made up of an infinite amount of lines. Twodimensional figures are called plane figures.
N
M
The line passing
through the points A
and B
is denoted by ⃡𝐴𝐵
THE CLERMONT SCHOOL
GEOMETRY RELEARNING WORKSHOP
SEVENTH
ACTIVITIES
B
1. Write 20 true propositions about the figure, use mathematical symbols.
Ex:
⃡ ∩ 𝑃 𝑎𝑡 𝑂
a. 𝑁𝑀
N
A
Y
Z
b. 𝐴𝐵 ∉ 𝑄
O
X
W
P
R
S
M
Q
2. Draw 10 couples of congruent figures. Write the math expression. Ex: ⧠𝐴𝐵𝐶𝐷 ≅ ⧠𝑅𝑆𝑇𝑈
A
D
R
S
B
C
T
U
THE CLERMONT SCHOOL
GEOMETRY RELEARNING WORKSHOP
SEVENTH
Angles
The word ‘angle’ is often used to mean the space between
two lines or a rotation.
Notation
∢𝐴𝐵𝐶 = ∢𝐵
For instance: the measure of the angle is 38 degrees, it is
denoted as: m∢ABC = 38°
Two angles are said to be congruent if their measure is the
same. If ∢𝐴𝐵𝐶 and ∢𝐸𝐹𝐺 are congruent, this is denoted as:
∢𝐴𝐵𝐶 ≅ ∡𝐸𝐹𝐺
Straight angle is a straight line. It has measure 180 °
Right angle is half of straight angle. It has measure 90 °
Acute angle is less than straight angle. It has measure less
than 90 °
Obtuse angle is bigger than straight angle and less than
straight angle. It has measure bigger than 90 ° and less than
180°.
Two angles are complementary if they add up 90°
Two angles are supplementary angles if they add up 180°
Straight angle is a straight line. It has measure 180 °
Right angle is half of straight angle. It has measure 90 °
Acute angle is less than straight angle. It has measure less
than 90 °
Obtuse angle is bigger than straight angle and less than
straight angle. It has measure bigger than 90 ° and less than
180°.
Adjacent angles are called angles like a and d, or a and b or b
and c or c and d Sum of adjacent angles are equal to straigth
angle(180°), so a = b and c = d.
Vertical angles are a and c or b and d. Vertical pair of angles
are equal i.e. a = c and b = d
Let's have two parallel lines intersected by third line. Angles
m and q or n and r or o and s or p and t are called
corresponding. They have the same measure.
THE CLERMONT SCHOOL
GEOMETRY RELEARNING WORKSHOP
SEVENTH