2. INDEX
• Introduction
• Angles In Daily Life
• Basic Terms And Definitions
• Intersecting Lines And Non
Intersecting Lines
• Perpendicular Lines
• Angles
• THEOREMS
• AKNOWLEDGEMENT
3. INTRODUCTION
• In math geometry the lines and
angles are important tools. If any
object in ideal, that is called as
line and it is represented as
straight curve.
• The angle is related with line that
is the cross-section of two-line is
create the angle and that
intersection point is called
as vertex. Here we see about
4. ANGLES IN DAILY LIFE
If we look around us, we will see angles everywhere.
5. BASIC TERMS AND DEFINITION
RAY: A part of a line, with one endpoint,
that continues without end in one direction
LINE: A straight path extending in both directions
with no endpoints
LINE SEGMENT: A part of a line that includes
two points, called endpoints, and all the points
between them
6. INTERSECTING LINES AND NON
INTERSECTING LINES
Intersecting Lines : Lines that
cross
Non Intersecting lines : Lines that
never cross and are always the same
distance apart
7. EXAMPLES OF NON INTERSECTING LINES
• Hardwood Floor
• Opposite sides of windows, desks, etc.
• Parking slots in parking lot
• Parallel Parking
• Streets: Laramie & LeClaire
9. ANGLES
In geometry, an angle is the figure formed by two rays sharing
a common endpoint, called the vertex of the angle. The
magnitude of the angle is the "amount of rotation" that
separates the two rays, and can be measured by considering
the length of circular arc swept out when one ray is rotated
about the vertex to coincide with the other.
Acute Angle
Right Angle
Obtuse Angle
Straight angle
Reflex Angle
Adjacent Angle
10. ACUTE ANGLES
The measure of an angle with a measure between 0°
and 90° or with less than 90° radians.
19. ADJACENT ANGLES
In geometry, adjacent angles, often shortened as
adj. ∠s, are angles that have a common ray coming
out of the vertex going between two other rays. In
other words, they are angles that are side by side,
21. PARALLEL LINES AND
TRANSVERSAL
Transversal :- A transversal, or
a line that intersects two or
more coplanar lines, each at a
different point, is a very useful
line in geometry. Transversals
tell us a great deal about
angles.
Parallel Lines :- Parallel lines remain the same distance
apart over their entire length. No matter how far you extend
them, they will never meet.
A B
C D
L
22. 1)LINEAR PAIR OF ANGLES
A pair of adjacent angles formed by
intersecting lines. Linear pairs of angles
are supplementary.
A
B
O
23. 2)VERTICALLY OPPOSITE ANGLE
In geometry, a pair of angles is said to
be vertical (also opposite and vertically opposite, which is
abbreviated as vert. opp. ∠s ) if the angles are formed
from two intersecting lines and the angles are not
adjacent. They all share a vertex. Such angles are equal
in measure and can be described as congruent.
24. 3)CORRESPONDING ANGLES
The angles that occupy the same relative
position at each intersection where a straight
line crosses two others. If the two lines are
parallel, the CORRESPONDING ANGLES are
AA
B
A=B
25. 4)ALTERNATE INTERIOR ANGLE
WHEN TWO PARALLEL LINES ARE CUT
BY A TRANSVERSAL, THE TWO PAIRS OF
ANGLES ON OPPOSITE SIDES OF THE
TRANSVERSAL AND INSIDE THE
A
B
A=B
26. 5)ALTERNATE EXTERIOR ANGLE
When two parallel lines are cut by a
transversal, the two pairs of angles on
opposite sides of the transversal and
outside the parallel lines, and the angles in
A
B
A=B
27. 6)CO-INTERIOR ANGLES
Interior angles on the same side of the
transversal are also referred to as consecutive
interior angles or allied angles or co-interior
angles. And there sum is always 180.
A
B
A+B=180
O
28. 7)ANGLE SUM PROPERTY
A
B C
The sum of the measures of the interior
angles of a triangle is 180. The diagram
above illustrates the Triangle Angle Sum
Theorem.
A+B+C+=180
O
29. 8)EXTERIOR ANGLE PROPERTY
A
B C
The exterior angle theorem is Proposition 1.16
in Euclid's Elements, which states that the measure of
an exterior angle of a triangle is greater than either of
the measures of the remote interior angles.
A+B=C
30. I would like to express my special thanks
of gratitude to my teacher (MRS.KRITI)
who gave me the golden opportunity to
do this wonderful project on the topic
LINES AND ANGLES, which also helped
me in doing a lot of Research and i came
to know about so many new things I am
really thankful to them.
Secondly i would also like to thank my
