LINES AND ANGLES...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. Almudena Casares

LINES AND ANGLES

www.matematicasalmudena.com Almudena Casares Fernández

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...


https://www.youtube.com/watch?v=k5etrWdIY6o


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



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



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.


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.


https://www.youtube.com/watch?v=UgfSwlqi4Qg

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.


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.


TYPES OF ANGLES


TWO IMPORTANT LINES

An angle bisector of an angle is a straight line

through a vertex which cuts the corresponding

angle in half.


TWO IMPORTANT LINES

A perpendicular bisector of a segment is a

straight line passing through the midpoint and

being perpendicular to it.


ANGULAR RELATIONSHIPS

Where two lines cross, the opposite angles are

equal.

ˆ ˆ ˆ1̂ 3 and 2=4



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.



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.


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.


ANGLES IN A POLYGON

The interior angles of a quadrilateral (a four-

sided shape) always add up to 360º.


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


ANGLES IN A POLYGON


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


https://www.youtube.com/watch?v=BPnP_EEZvQc

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


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



Collorary:

Any angle inscribed in a semi-circle is a right angle.


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


https://www.youtube.com/watch?v=vEro2-qcFqU

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


Documents

LINES AND ANGLES...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. Almudena Casares