Lines And AnglesBy

Hardik KapoorClass :- IX – A

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

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.

Angles in daily life

If we look around us, we will see angles everywhere.

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

An Exact Point Or Location

POINTS

Intersecting Lines And Non Intersecting Lines

Intersecting Lines : Lines that cross each other.

Non Intersecting lines : Lines that never cross and are always the same distance apart. They are also called parallel lines.

Examples Of Non Intersecting Lines

• Hardwood Floor• Opposite sides of windows, desks, etc.• Parking slots in parking lot• Parallel Parking

Perpendicular lines

Two lines that intersect to form four right angles

Examples Of Perpendicular Lines

• Window Panes• Streets Of Cities

AnglesIn 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

Acute Angles

The measure of an angle with a measure between 0° and 90°.

Examples Of Acute Angles

Right angle

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

Examples Of Right Angle

Obtuse Angle

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

Examples Of Obtuse Angle

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)

Examples Of Straight Angle

Reflex Angle

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

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.

Linear Pair Of Angles

A pair of adjacent angles formed by intersecting lines. Linear pairs of angles are supplementary.

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.

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

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.

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.

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.

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.