Alternate Angles

Concept Explanation

Alternate Angles

Two angles, formed when a line crosses two other lines, that lie on opposite sides of the transversal line and on opposite relative sides of the other lines. If the two lines crossed are parallel, the alternate angles are equal.

Alternate interior angles: Alternate interior angles are the pair of angles lying in the region between the two lines (intersected by a transversal) and on the opposite sides of the transversal but one below the transversal and the other above the transversal. In the adjoining figure $large (angle 4&angle 5)$ and $(angle 3&angle 6)$ are pair of alternate interior angles.

Theorem: If a transversal intersects two parallel lines, then each pair of alternate interior angles is equal.

Given: m and n are parallel lines and the transversal l cuts m and n

To Prove : $large angle 3 = angle 6 ;and; angle 4= angle 5$

Proof: Corresponding angles are equal as m and n are parallel lines and l is the transversal

$large angle 1 = angle 5 ;and; angle 2= angle 6;;;;;(1)$

Vertically opposite angles are equal when m and l intersect.

$large angle 1 = angle 4 ;and; angle 2= angle 3 ;;; .......(2)$

From Eq. (1) and (2)

$large angle 5 = angle 4 ;and; angle 6= angle 3$

Hence Proved that alternate interior angles are equal.

Theorem: If a transversal intersects two lines such that a pair of alternate interior angles is equal, then the lines are parallel.

Given : m and n are lines and the transversal l cuts m and n and $angle 3 = angle 6$

To Prove : m and n are parallel lines

Proof: Vertically opposite angles are equal when m and l intersect.

$angle 2= angle 3 ;;; .......(1)$

and $angle 3 = angle 6;;;;.....(2)$

From Eq. (1) and (2)

$angle 2 = angle 6$

But they are Corresponding angles as m and n are lines and l is the transversal and as they are equal the lines are parallel.

Hence Proved that m and n are parallel lines.

Same is the case with exterior alternate angles

Alternate exterior angles: Alternate exterior angles are the pair of angles lying outside the region between the two lines (intersected by a transversal) and on the opposite sides of the transversal but one below the transversal and the other above the transversal. In the given figure $(angle 1&angle 8)$ and $(angle 2&angle 7)$ are pair of alternate exterior angles.

Illustration: Find the angle which is alternate to : $angle 7,angle 6;and ;angle 1$

Solution:

Angle alternate to $angle 7$ = $angle 2$ , these are alternate exterior angles

Angle alternate to $angle 6$ = $angle 3$ , these are alternate interior angles

Angle alternate to $angle 1$ = $angle 8$ , these are alternate exterior angles

Illustration: In the given figure m || n and $large angle 1:angle 2$ = 5:3. Find the value of $large angle 3$ .

Solution: $angle 1 : angle 2 = 5: 3$

Let the common factor be x

$angle 1 = 5x; and ; angle 2 = 3x$

$angle 1 + angle 2 = 180^0 [ Linear; Pair]$

$5x + 3x = 180^0$

$8x = 180^0$

$x = frac{180^0}{8} = frac{45^0}{2}$

$angle 2 =3frac{45^0}{2}= frac{135^0}{2}$

$angle 2 = angle 3; [ Alternate ;angle ]$

$angle 3 = frac{135^0}{2}$

Illustration: In the given figure, PQ and RS are two mirrors placed parallel to each other . An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path and strikes the mirror RS at C and again reflects back along CD. Prove that AB || CD.

Solution:

.... (More Text Available, Login?)

Sample Questions

(More Questions for each concept available in Login)

Question : 1

Find the alternate angle to c:
A. b	B. a	C. d	D. f
Right Option : C
View Explanation

Question : 2

Find the value of e:
A. 60	B. 120	C. 65	D. 120
Right Option : C
View Explanation

Question : 3

Find the alternate angle to d:
A. c	B. f	C. 65	D. g
Right Option : A
View Explanation

Video Link - Have a look !!!

Language - English

Chapters

Time, Speed and Distance

Problems On Boats And Stream

Rules For Divisibility

Square and Square Root

Surface Area and Volume

Simple and Compound Interest

Profit Loss and Discount

Content / Category

IMO-Mathematics Olympiad

Central Government Service

ISO - Science Olympiads

State Government Services

Banking And Insurance

Railways & Metro Services

MBA Entrance

Law Entrance

English Proficiency

Reasoning Proficiency

Computer Proficiency

Navodaya Entrance 6th & 9th

Sainik School Entrance

Andhra Bank

Class / Course

General Awareness For SSC

SSC CHSL

General Knowledge For SSC

SSC MTS

SSC CHSL Test Series

SSC CGL

Students / Parents Reviews [20]

We started with lot of hope that Abhyas will help in better understnding of complex topics of highers classes. we are not disappointed with the progress our child has made after attending Abhyas. Though need to mention that we expected a lot more. On a scale of 1-10, we would give may be 7.

Manya

8th

My experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak poi...

Shivam Rana

7th

It was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.

Cheshta

10th

Abhyas is good institution and a innovative institute also. It is a good platform of beginners.Due to Abhyas,he has got knoweledge about reasoning and confidence.My son has improved his vocabulary ...

Manish Kumar

10th

Abhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.

Manish Kumar

10th

My experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.

Ayan Ghosh

8th

One of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develo...

Aman Kumar Shrivastava

10th

Abhyas institute is one of the best coaching institute in the vicinity of Ambala cantt.The institute provides good and quality education to the students.The teachers are well experienced and are v...

Abhyas institute is one of the best coaching institute in the vicinity of Ambala cantt.The institute provides good and quality education to the students.The teachers are well experienced and are very helpful in solving the problems. The major advantages of the institute is extra classes for weak...

Shreya Shrivastava

8th

Third consective year,my ward is in Abhyas with nice experience of admin and transport support.Educational standard of the institute recumbent at satisfactory level. One thing would live to bring in notice that last year study books was distributed after half of the session was over,though study ...

Ayan Ghosh

8th

My experience with Abhyas academy is very nice or it can be said wonderful. I have been studying here from seven class. I have been completing my journey of three years. I am tinking that I should ...

Hridey Preet

9th

Abhyas is an institute of high repute. Yogansh has taken admission last year. It creates abilities in child to prepare for competitive exams. Students are motivated by living prizes on basis of per...

Yogansh Nyasi

7th

It was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.

Eshan Arora

8th

Being a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from m...

Prisha Gupta

8th

It has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice

Barkha Arora

10th

I have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying

Yatharthi Sharma

10th

The experience was nice. I studied here for three years and saw a tremendous change in myself. I started liking subjects like English and SST which earlier I ran from. Extra knowledge gave me confi...

Aman Kumar Shrivastava

10th

About Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has...

Shreya Shrivastava

8th

In terms of methodology I want to say that institute provides expert guidence and results oriented monitering supplements by requsite study material along with regular tests which help the students to improve their education skills.The techniques of providing education helps the students to asses...

Aman Kumar Shrivastava

10th

A marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre f...

Archit Segal

7th

Usually we see institutes offering objective based learning which usually causes a lag behind in subjective examinations which is the pattern followed by schools. I think it is really a work of planning to make us students grab the advantages of modes of examination, Objective Subjective and Onli...

Anika Saxena

8th

View All

Attention !!!!!