1. By Madhu Narayan K.V.Hebbal Bangalore Region
Lines And Angles By
Madhu Narayan
K.V.Hebbal
Bangalore Region

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. If we look around us, we will see angles everywhere.
Angles in daily life
If we look around us, we will see angles everywhere.

5. Basic Terms And Definition
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
RAY: A part of a line, with one endpoint, that continues without end in one direction

6. POINTS
An Exact Point Or Location

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

9. Perpendicular lines
Two lines that intersect to form four right angles

10. Examples Of Perpendicular Lines
Window Panes
Streets Of Cities

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.

13. Examples Of Acute Angles

14. Right angle
An angle formed by the perpendicular intersection of two straight lines; an angle of 90°.

15. Examples Of Right Angle

16. Obtuse Angle
Angle measures greater than 90 degrees but less than 180 degrees.

17. Examples Of Obtuse Angle

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)

19. Examples Of Straight Angle

20. A Reflex Angle is more than 180° but less than 360°

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.

29. The end of This presentation
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