PYTHAGORAS THEOREM| EASY EXPLANATION| CLASS 7| INSIGHTFUL MATHS
PYTHAGORAS THEOREM| EASY EXPLANATION| CLASS 7| INSIGHTFUL MATHS
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00:00hey everyone welcome to insightful maths I hope you all are enjoying the videos
00:06I am uploading on different topics and for different grades so if you have not
00:11liked and subscribed to the channel please do it right now for getting more
00:16informative videos. Topic for today is Pythagoras theorem it is basically the
00:21topic which is being introduced in grade 7 so we are going to discuss this topic
00:26I request please see the video till end to understand this topic and the
00:31application so let's begin you can see on the slide this theorem basically is
00:38named after a Greek mathematician called Pythagoras so you should know if we are
00:44talking about Pythagoras theorem it is based on the name of a Greek
00:49mathematician whose name was Pythagoras this you should know another thing is
00:55when we are talking about Pythagoras theorem this is applicable only in the
01:01case of a right angle triangle I hope everyone is aware what is a right angle
01:06triangle where one angle of the triangle is 90 degree the right angle okay so
01:13what this theorem does it gives us a relationship between the different sides
01:18of a right angle triangle let's take it further the Pythagoras theorem says that
01:25the sum of the square of the sides of a right angle triangle is equal to the
01:31square of the hypotenuse now what is this such a big statement it sounds
01:36little confusing but it is really very easy have a look at this picture is it a
01:41right angle triangle and it is right angle here in between the sides A and B
01:47let us first understand how do we name these sides in a right angle triangle
01:54the length which is just opposite to the right angle triangle this name is
01:59known as hypotenuse please have a look at the spelling this longest side of a
02:06right angle triangle which is just opposite to your right angle is called
02:11hypotenuse another two sides are known as the arms or one is height another is
02:18base whichever manner longest side is hypotenuse other two are arms generally
02:24this resting one this is which is joined to the base that is the base of a right
02:30angle triangle and this side A is the height this much is understood so what
02:36does the theorem says the square of the longest side which is the longest side
02:42here that is C so longest side square hypotenuse square is equal to the sum
02:49sum means I am adding two number which two number the squares of the other two
02:56side one side is of length a so I will take a square another side is B I will
03:03take B square so how do I frame the statement in a right angle triangle it
03:09is important to note down here in a right angle triangle the square of the
03:14hypotenuse is equal to the sum of square of other two sides you can frame it in
03:22this manner and who has given this property or the theorem it is named
03:27after the Greek mathematician Pythagoras taking this further let us
03:33understand why does this happen this is the proof of Pythagoras theorem let us
03:39consider that we have a right angle triangle you can see this yellow one it
03:43is a right angle triangle three different squares are attached to the
03:49three different sides of this right angle triangle this is the square you
03:53can see here this is the square attached to A square attached to B and square
03:59attached to C how do we find the area of a square area of a square is side into
04:06side so what is the area of C have a look how many what is the length of the
04:11side 1 2 3 4 5 it's a square if one side is 5 so 5 into 5 25 is the square the
04:21area of this one in the similar manner 1 2 3 and 1 2 3 3 into 3 is 9 area of this
04:30block is 9 in the similar manner 1 2 3 4 and 1 2 3 4 the area of this block is
04:384 into 4 16 do we and what is the area how do we find area if the side is C C
04:47into C area is C square here B into B area is B square and A into A area is A
04:56square here let us see if actually there is a relationship between these three
05:00numbers as per Pythagoras the longest side square that means 25 I'm not taking
05:0725 square the side is 5 and 5 square is 25 I have already taken the square okay
05:15so 25 should be equal to the sum of the other two what is A square here 16 and
05:23what is the B square given it is equal to 9 16 plus 9 wow that is coming 25
05:31both the sides are coming 25 only that means it is true so this is the proof of
05:36Pythagoras theorem we should understand the square of the longest side that is
05:42hypotenuse is equal to the sum of the square of other two sides now let us
05:49understand why we are actually learning this what is the use of learning
05:54Pythagoras theorem it determining the length of the side for example we have a
06:00right angle triangle if any two sides are given we can easily find the length
06:05of the third side for example A and B is known I can find C if C and B is known I
06:12can find A if C and A is known I can find B so in a right angle triangle if
06:18any two sides are given you can easily find the length of the third side to
06:24calculate the distance between two points in a coordinate system what is a
06:29coordinate system it looks I'll make it sure it looks something like this when
06:34we draw a bar graph on a graph paper what do we generally do we make some X's
06:39and then the bar this is basically the X 1 and the Y 1 these are the coordinate
06:46axis so if I have any two points here on the coordinate axis I can easily find
06:53the distance between two points using the Pythagoras property you are going to
06:58learn this in grade 10 so I am not touching it as of now but definitely in
07:04the next video I am going to cover this topic if anyone is interested to watch
07:08that please watch another video okay third one is it is basically used in
07:14construction and engineering ensuring that the structures are built correctly
07:19especially when dealing with the right angles and the diagonal bracing okay so
07:24basically in the construction work engineers generally use this property to
07:29ensure if the calculation is going correct navigation and surveying also
07:35uses this property to calculate the shortest path or the mapping distances
07:40in the navigation also it is being used I'll give you a practical application of
07:46this one here you can see that it is a wall right I hope you are able to see
07:50this white wall and there is a ladder here and there this ladder is lean
07:55against the wall okay are we able to make out that this is the vertical line
08:01and this is the ground the angle formed between the wall and the ground is it 90
08:10degree you can have a look around in your house and you can easily make out
08:14if this is the wall and this is the ground always the angle between these
08:18two is 90 degree so if this is 90 degree and the ladder is lean like this so
08:26which is the hypotenuse here if I need to know the length of the ladder what do
08:32I do besides making the right angle triangle one will be height one will be
08:38base so which is the longest side here hypotenuse or the longest side is the
08:44ladder here okay so all these ladder questions you need to understand this
08:50that this one is your hypotenuse ground is your base the distance between the
08:57base of the wall and the base of the ladder this distance is your base and
09:03this one is your vertical height let us do some questions to make you
09:08understand this concept well but a prerequisite the minimum requirement for
09:14doing this is you should know very well how to find the squares and the square
09:19root of the number which I am not covering right now I have already made
09:25the separate video on square and square root you can go to my channel and have a
09:29look there so you can easily understand how to find the square and square root
09:33of any number that will be applicable your hundred percent so have a look at
09:39question number one a right angle triangle has legs of length 6
09:43centimeter and 8 centimeter you need to tell what is the length of the
09:48hypotenuse so let us make it is always advisable to make a figure okay it gives
09:56more of clarity to you only you will find it much easier to solve the
10:01questions when the figure is there in your mind okay the legs are 6 centimeter
10:07and 8 which ever you can take if you wish to take this vertical as 6 you can
10:12if you wish to take base as 6 you can answer will be same let's say this is 6
10:18centimeter another is 8 centimeter question says what is the length of the
10:25hypotenuse I need to find the longest side so how will you start you will
10:30write here using Pythagoras theorem you have to first write Pythagoras theorem
10:37you have to mention here using Pythagoras theorem what do we know the
10:46square of the hypotenuse what is the hypotenuse here AC so you have to
10:51mention here longest side square is equal to the sum of which two side
10:57square a b a to a b square and another side is b c square I hope everyone is
11:07able to understood till here now just input the values you need to find a c
11:12square a b is what it is 6 so that is 6 square b c is 8 it is 8 square
11:20the square means the number multiplied by itself so what is 6 square it is 6
11:26into 6 that is 36 so this number is 36 8 square is 8 into 8 that is 64 if I add
11:36these two numbers that will give me 100 so a c square is equal to 100 if there
11:43is a square on one side and I need to remove this square it goes as under root
11:50on another side so the value of a c is under the root or square root of 100 how
11:57do we find square root if two similar numbers are there inside the root under
12:03root cancel one number cancel and one will come out I request please go and
12:08see that video made on square and square root you can easily solve this question
12:13so this is under the root 10 into 10 two similar numbers under root cancel
12:1910 cancel and only 10 will be left out so the value of a c is 10 don't forget
12:26to write the unit units mentioned here are centimeter so answer is 10 centimeter
12:32easy enough let's move to another question in a right angle triangle now
12:39the hypotenuse is given to you in a right angle triangle the hypotenuse is
12:4410 meters long let me just make it for you so that you can easily relate what
12:50all values are being given this value is 10 meter one leg is 6 meter up kissing
12:57for the 6 list if you hardly makes any difference let's say it is 6 meter you
13:02have to find the length of the other leg this one is missing that you need to
13:06find first of all give it the name ABC this is a right angle triangle right
13:13angle at B why because the longest side is just opposite to this right angle
13:19triangle and it is given to you as 10 again you write using Pythagoras
13:26property what does it says a c square hypotenuse square is equal to a b square
13:35plus BC square whatever values you know put the values here what is AC it is 10
13:43so you have to write 10 square is equal to I do not know a B keep it like this
13:50plus BC is 6 so 6 square find the value 10 square in the previous question we
13:58have done 10 square is for 10 into 10 hundred which is a b square plus 6
14:04square is 36 now if a number is being added on one other side and I take it to
14:12another side transposing it plus become minus minus become plus it is plus 36 so
14:20if I take plus 36 on another side it will be hundred minus 36 which is a b
14:27square the difference of these two numbers is 64 which is a b square I told
14:35you if we have to remove this square it goes as square root of this number so
14:42this is square root of 64 which is a b that means two similar numbers inside
14:50the root 64 is what 8 into 8 is 64 two similar numbers so one number cancel
14:58under root cancel we are left with just 8 and the unit here is meters so our
15:04answer is 8 meter so we have got this value this answer is 8 meter let's move
15:12to now the different kind of the question a triangle has sides of length
15:175 12 and 13 it is not given what is the hypotenuse what is the base nothing is
15:23being given just the length of three sides are given question is asking is it
15:28a right angle triangle we know that Pythagoras properties applicable only in
15:34the case of right angle triangle one more thing we know very well that always
15:39the longest side is the hypotenuse so out of these three which side should I