# LINES & ANGLES || Part 1 – Introduction || NCERT – Class 9 – Mathematics || Hindi

Friends subscribe to our channel And press the bell icon First to see our latest videos Hello friends and welcome to Vidya Vision Institute My name is Himanshu and friends, from this video of today we will start Chapter 6 Lines & Angles The first part of which is introduction. Friends, in this video we are going to read about basic definitions and basic concepts of lines & angles So let’s start Friends, first of all let’s understand Lines. What is a line? as if this is a line, what are the properties of this line now? Friends, a line is always straight The line is always straight has no thickness The line has no width extend in both directions and it extends in both directions and has no ends and it has no end once more a line is always straight has no thickness extend in both directions and has no ends So here is the definition of line Now friends if there is a one end of a line and the other end is not there then we call that line ‘Ray’ Like this is a starting point… A Now a line starts from here and there is no end of it So we call it ‘Ray’ there is a very good example of this Like flashlight Whenever we turn a flashlight on Rays come out of it Which has a starting point but not an end point The same way if a line has two ends So we call it ‘line segment’ As if this is a line and it has two end points are A and B That is why we will call it ‘Line Segment’ So friends ‘line’ mean which has no end point. Ray means which has one end point.. starting point And Line Segment Which means there are two end points it is ending on both sides So here is line, ray, and Line Segment [INTERSECTING AND NON-INTERSECTING LINES] Now friends what is intersecting and non-intersecting lines Friends, if there are so many lines on a plane surface Then they will either be intersecting or non-intersecting that means that they will be parallel Lines can be of two types, either intersecting or parallel. now as these two lines are L and M Intersecting each other so we will call them “Intersecting Lines” in the same way These two lines are P and Q It is parallel between the two and will never intersect each other That’s why we will call it “Non – Intersecting Lines” or parallel lines Friends, we have understood “Intersecting” and “Non – Intersecting Lines” Now friends let’s understand that what are “collinear” and “non-collinear points” If three or more points lie on the same line then they are called collinear points otherwise they are called non-collinear points once again If three or more points lie on the same line, they are called collinear points. otherwise they are called non-collinear points That is, if any three points are on the same line then we will call them collinear points otherwise they will be non-collinear points For example, here are 3 points A, B and C. In the same way these 3 points are P, Q and R Now as we can see These all three points A, B, C are on the same line. so we will call them collinear points and P, Q, R are not in a straight line so we will call them non-collinear points Point A B & C are Colinier Points and point P Q & R are non-collinear points. Let’s go ahead Now friends, let’s discuss about Angles so far we have discussed about the lines Now let’s read about Angles Friends what exactly is an Angle? How are Angles are made? When two rays are originated from the same point an angle is made That is, when two rays emanate from the same point Then an angle is made such as if these are two rays It is leaving from the same point And here an angle is formed The corner point is called vertex And the point where the rays are coming out We call it vertex Here is “Vertex” and the rays making an angle is called arm and the rays that are making that angle We call it the arm of the angle such as these are the arms of the angle Let’s check it out once more The corner point is called vertex and the rays making an angle is called arm so this is the definition of Angle Now let’s learn about ‘Types of Angle’ How many types of angles are there Types of Angle is nothing but.. Angles are separated according to their size The first one is Acute Angle Friends, here is our Acute Angle All Angles that are more than zero degrees and less than 90 degrees We call them Acute Angle Friends there is a very easy way to remember ‘Acute Angle’ Acute word starts with “A” And the angle formed between ‘A’ is ‘Acute ‘Angle. Here’s our Acute Angle This way you will always remember Acute Angle Now friends next is right angle We call 90 degree Angle as Right Angle. Right Angle ie 90 degree In the same way, now we will move beyond 90 degrees Then you will get obtuse angle Angle that is greater than 90 degrees and less than 180 degrees We call it obtuse angle Here is our obtuse angle greater than 90 degrees and less than 180 degrees Our straight Angle is next in the same way The angle of 180 degrees is called straight Angle. Here is our straight Angle Ie the angle through which a straight line is drawn We call it Straight Angle Straight Angle=180 degrees And next is Reflex Angle Over 180 degrees and below 360 degrees We call it Reflex Angle greater than 180 degrees and less than 360 degrees is called reflex angle Now guys pay attention Is it Angle A B C is it Acute Angle or Reflex Angle? Now if you measure this Angle from here to here Then you will get Acute angle And if we don’t get it from here, you will get it Reflex angle It is also Angle ABC Acute Angle, it is also Reflex Angle It just depends on which side it is and which is the second arm. How you measure it depends on And friends, sometimes such questions are also asked. In which you are given the value of Acute Angle And you are asked to tell the value of its Reflex Angle. And in that case it’s very easy Reflex angle=360 degree – interior angle If you know the value of Interior Angle So subtract it from 360 degrees You will know the value of Reflex Angle Let’s go ahead Now we read complementary angles Now what are these complementary angles? when sum of two angles is 90 degree then they are called complementary angles once more when sum of two angle is 90 degree then they are called complementary angles That means if any two angles are 90 degrees joining them We shall call it complementary angles. Like this is the Angle ABC which is 30 degrees And this is an angle PQR is 60 degrees So 60 + 30 is 90 So Angle ABC and PQR will become complementary angles. In the same way, there is a complementary angle. when sum of two angles is 180 degrees then they are called supplementary angles Ie if the sum of two angles is 180 degrees Then we will call it supplementary angle As if this angle is ABC 120 degrees And in the same way it’s an angle PQR it’s 60 degrees So ABC and PQR will be supplementary angles Now friends Complementry and supplementary, confuse Don’t need to be confused at all Is very easy Complementry starts from C and Conner from C And Conner is 90 degrees once again Complementry starts with C And C is Conner And how much is Conner? Conner is always 90 degrees Supplementary starts with the letter ‘S’ in the same way And what happens with ‘S’ is from ‘S’ And the straight line is always 180 degrees So let’s go Friends, so far we have discussed the line ray and line segment And we discussed Angles, Acute Angel, Right Angle, Obtuse Angle and Reflex Angle And we discussed about Complementary Angle and Supplementary Angle And friends, now we will discuss very important topics That is Adjacent Angles Adjacent Angles (adjacent angles) are very important subjects And also very interesting So let’s start with Adjacent Angles two angles are called adjacent angles when they have common vertex one common arm and don’t overlap Once again friends Two Angles will be Adjacent Angles If they have a common vertex Have a common arm And they don’t overlap each other Like you see this figure Look at it there are two angles The first one is Angle X And the other one is Angle Y Angle X and Angle Y both have a common vertex And have a common arm And don’t overlap each other So Angle X and Angle Y will be Adjacent Angle Now friends, watch this Figure carefully And find out whether Angle x and Angle y, Will there be Adjacent Angles? No Angle X and Angle Y will not be Adjacent Angles Although they have a common vertex But there is no common arm Let’s see the next figure guys Now friends, see here Will there be Angle X and Angle Y Adjacent Angles? No There will also be no Angle X and Angle Y Adjacent Angles. Now look at the common arm But not common vertex Let’s see the next figure guys See this figure This figure is in exactly the same way as I said in the example Now it will see Angle X is ABD and Angle y is ABC Now look at Angle X and Angle Y Will there be Adjacent Angles? No These too will not be adjacent angles here. It also has common arm common vertex is also common arm is in it AB common vertex is B But both X and Y overlap Angle Y that is overlapping on Angle X So these two will not be Adjacent Angles Let us now discuss the properties of Adjacent angle. Properties of the Adjacent Angle As if it is a figure ABCD And this is an Angle X and this is an Angle Y And this is another Angle we call Angle Z Angle ABC Done Angle Z So this is the property of Adjacent Angle That Angle x + Angle y=Angle z Ie when two angles are adjacent then their sum is always equal to the angle formed by the non common arm once more when two angles are adjacent then their sum is always equal to the angle formed by the non – common arm Which means that non-common arm will become Angle. Now see here the non-common arm is AB and BC And this will become the Angle ABC What will be its value It will be equal to the sum of both adjacent angles. This is the property of the adjacent angle. And very important quality Many questions are asked on this Friends this is it for this video Hope you liked the video Friends we will discuss in the next video Linear Pair Axiom Friends Linear Pair Axiom is a very important subject And is a very interesting subject Thanks for watching this video guys Hope you liked my video Please if you liked the video guys Like my video Share with your friends Subscribe to my channel How did you like the video? Let me know in the comment section. thank you so much and take care

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Meaning of overlap

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Angle x and a y not agested angle