lines and angles...angles in a polygon a polygon is a 2d shape with straight sides. the interior...
TRANSCRIPT
LINES AND ANGLES
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BASIC GEOMETRIC ELEMENTS
VIDEO https://www.youtube.com/watch?v=k5etrWdIY6o
A point only indicates a position and has no size.
Points are usually denoted with capital letters: A, B, C…
A line is a long thin mark made by a pen, pencil, etc.In geometry a line:• is straight (no curves), • has no thickness, and • extends in both directions without end (infinitely).
Lines are usually denoted with lower case letters: r, s, t...
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BASIC GEOMETRIC ELEMENTS
A ray is a line with a starting point but no endpoint (it
goes to infinity). A point divides a line into two parts;
each one (with the vertex) is a ray. The point A is the
origin.
A segment (line segment) is a piece of a straight line
any between two points on the line.
A
BA
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BASIC GEOMETRIC ELEMENTS
A plane is a flat surface with no thickness.
It extends forever. We often draw a plane with edges,
but it really has no edges.
A half-plane or semiplane is each part in which a
plane is divided by a straight line.
Half-plane
Half-plane
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BASIC GEOMETRIC ELEMENTS
Lines are parallel if
they are always the
same distance apart
(called "equidistant"),
and will never meet.
Intersecting lines are
lines that have one
point in common.
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WHAT IS AN ANGLE?
VIDEO https://www.youtube.com/watch?v=UgfSwlqi4Qg
An angle is a measure of turn. It is formed whentwo lines meet.
The lines are called arms and the point wherethey meet is called a vertex.
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MEASUREMENT OF ANGLES
A (sexagesimal) degree is the 360th part of a circumference. The degree is a unit of measurement to measure angles.
A minute is the 60th part of a degree and a second is the 60th part of a minute.
A protactor is
an instrument
used to
measure
angles.
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TYPES OF ANGLES
A right angle is an angle which is equal to 90°. It’s a
quarter of a turn.
A straight angle is a 180° turn.
A full rotation is an angle of 360º.
An angle that is less than a right angle is called an
acute angle.
An angle that is more than a right angle and less
than a straight angle is called an obtuse angle.
An angle that is more than a straight angle is called
a reflex angle.
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TYPES OF ANGLES
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TWO IMPORTANT LINES
An angle bisector of an angle is a straight line
through a vertex which cuts the corresponding
angle in half.
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TWO IMPORTANT LINES
A perpendicular bisector of a segment is a
straight line passing through the midpoint and
being perpendicular to it.
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ANGULAR RELATIONSHIPS
Where two lines cross, the opposite angles are
equal.
ˆ ˆ ˆ1̂ 3 and 2=4
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ANGULAR RELATIONSHIPS
Any two angles that add up to 180 degrees are
known as supplementary angles.
Property: Two angles whose arms are parallel or they
are the same or they are supplementary.
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ANGULAR RELATIONSHIPS
Two parallel lines and another line crossing
1=3; 2=4;5=7; 6=8. They are called vertically opposite angles.
1=5; 2=6; 4=8; 3=7. They are called corresponding angles.
1=7; 4=6. They are called external alternate angles.
2=8; 3=5. They are called Internal alternate angles.
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ANGLES IN A POLYGON
A polygon is a 2D shape with straight sides.
The interior angles of a triangle (a three-sided
shape) always add up to 180º.
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ANGLES IN A POLYGON
The interior angles of a quadrilateral (a four-
sided shape) always add up to 360º.
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ANGLES IN A POLYGON
The interior angles on an n-sided polygon is
(n-2)·180. (It can be found by dividing the shape into
n-2 triangles)
Each angle in a n-sided regular polygon measures:
2 ·180n
n
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ANGLES IN A POLYGON
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THE CIRCUMFERENCE
An arc is a portion of the
circumference.
A chord is a line
segment that links two
points on a circumference.
If it passes thought the
centre then it is called
diameter.
The radius is a line from
the center of a circle to a
point on the circumference.
VIDEO https://www.youtube.com/watch?v=BPnP_EEZvQc
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ANGLES IN A CIRCUMFERENCE
A central angle is the one formed between the two
radios drawn from two points on the circumference;
so a central angle has its vertex in the centre of the
circumference.
AC AOC
ANGLES IN A CIRCUMFERENCE
A inscribed angle is the one formed between the two
lines drawn from the ends of the chord making the
segment to any point on the circumference of that
segment.
A B1
2
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ANGLES IN A CIRCUMFERENCE
Collorary:
Any angle inscribed in a semi-circle is a right angle.
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AXES (LINES) OF SYMMETRY
The two sides of a graph on either side of the axis of
symmetry look like mirror images of each other.
VIDEO
https://www.youtube.com/watch?v=vEro2-qcFqU
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AXES (LINES) OF SYMMETRY
A regular polygon has all sides equal, and all angles
equal.
A regular polygon of n sides has n .Lines of Symmetry
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