F.A-2 ACTIVITY-2LINES AND ANGLES

SUBMITTED TO MRS.KRITI

SUBMITTED BY:-7)ARMAN BENIPAL8)BHARAT NANDA9)BISMANOT SINGH10)CHASHMEET SINGH11)CHIRAG SHARMA12)DIVYAM GOYAL

INDEX• Introduction• Angles In Daily Life• Basic Terms And Definitions• Intersecting Lines And Non

Intersecting Lines• Perpendicular Lines• Angles• THEOREMS• AKNOWLEDGEMENT

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

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

EXAMPLES OF NON INTERSECTING LINES

• Hardwood Floor• Opposite sides of windows, desks, etc.• Parking slots in parking lot• Parallel Parking• Streets: Laramie & LeClaire

PERPENDICULAR LINES

TWO LINES THAT INTERSECT TO FORM FOUR RIGHT ANGLES

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 AngleRight Angle

Obtuse AngleStraight angleReflex Angle

Adjacent Angle

ACUTE ANGLES

The measure of an angle with a measure between 0° and 90° or with less than

90° radians.

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)

180O

EXAMPLES OF STRAIGHT ANGLE

REFLEX ANGLE

A REFLEX ANGLE IS MORE THAN 180° BUT LESS THAN 360°

230O

A

B

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.

THEOREMSA GENERAL PROPOSITION NOT SELF-EVIDENT BUT PROVED BY A CHAIN OF REASONING; A TRUTH ESTABLISHED BY MEANS OF ACCEPTED TRUTHS.

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

1)LINEAR PAIR OF ANGLES

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

angles are supplementary.A

B

A+B=180O

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.

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

equal.

AA

B

A=B

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 PARALLEL LINES, AND

THE ANGLES IN EACH PAIR ARE CONGRUENT.

AB

A=B

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 each pair are congruent.

A

B

A=B

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.

AB

A+B=180O

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+=180O

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

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 parents and friends who helped

me a lot in finalizing this project within the limited time frame.