2. Lines and angles
• Introduction
• Angles In Daily Life
• Basic Terms And Definitions
• Points
• Intersecting Lines And Non
Intersecting Lines
• Perpendicular Lines
• Angles
• Parallel Lines And A Transversal
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 types of line and angle in
math.
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
7. 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
8. Examples Of Non Intersecting
Lines
• Hardwood Floor
• Opposite sides of windows, desks, etc.
• Parking slots in parking lot
• Parallel Parking
• Streets: Laramie & LeClaire
11. 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 Angles
•Linear Pair Of Angles
•Vertically Opposite Angles
12. Acute Angles
The measure of an angle with a measure
between 0° and 90° or with less than
90° radians.
18. Straight Angle
A straight angle changes the direction to point the
opposite way. It looks like a straight line. It
measures 180° (half a revolution, or two right
angles)
21. 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, or
adjacent.
22. Linear Pair Of Angles
A pair of adjacent angles formed by intersecting
lines. Linear pairs of angles are supplementary.
23. 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. 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.
•Corresponding Angles
•Alternate Interior Angles
•Alternate Exterior Angles
•Interior Angles On The Same Side Of the transversal
25. 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 equal.
26. 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 parallel lines, and the
angles in each pair are congruent.
27. 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 each pair are congruent.
28. Interior Angles On The Same
Side Of the transversal
Interior angles on the same side of the transversal are also
referred to as consecutive interior angles or allied angles or
co-interior angles. Further, many a times, we simply use the
words alternate angles for alternate interior angles.
