Understanding Triangle Properties and Types

Hello guys, this is Marci from Evidyadi Church and I'm starting with the chapter number 6. Name of the chapter is Triangle and its Properties. So this is an introduction video in which we will discuss all the concepts in this chapter. So that when you do exercises questions, you will find them very easy. Now, the chapter's name is Triangle and its Properties. On properties, first we will know what is triangle. Triangle we all know. It is a closed figure or a closed curve which has three line segments. So this can be a triangle. Similarly this can be a triangle. So there are many shapes of a triangle which is possible. So if three line segments are joining then that is a triangle. Also it is a closed figure. Okay. Now here also there are some parts of triangle. Like first of all let's talk about side. Let's take this triangle. Let's name it PQR. Now what are the sides of this triangle? PQ is the side. Sides are its line segments. So PQ. Similarly QR. Then we have PR. So these are the sides of the triangle. Next is angles. Now in triangles we have angles. Angles are Angle P, angle Q, angle R. So if I write angle P, it can be written as angle Q, P, R. Or angle R, P, Q, making sure that P comes in between. Similarly, angle P, angle Q, angle R. Okay, so these are angles of triangle. Next we have The vertices of triangle. Now what are vertices? You must have read vertex. So vertex are corner points. Like in this triangle, this is the corner point, this is the corner point and this is the corner point. So these corner points are vertex of triangle or we can say vertices of triangle. So the vertices are P, Q, R. Right? These are the vertices of triangle. Okay, so this was a short introduction about what are triangles Now let's come to some more topics and concepts which will be discussed in this chapter So the next topic is Median So we will discuss what is Median of Triangle What is the Median of Triangle? When a line connects any vortex of a triangle with the midpoint of its opposite side Now it must be very confusing, let's understand it with a figure So here is a triangle Now any of its vortexes, where is the vortex? This is the vortex, this is the vortex and this is the vortex So a line which starts with a vortex, let's suppose we are starting with this vortex So it will pass through from here and the opposite side of this vortex is this At its midpoint, so this is triangle AB C and this cone is point D So the biggest thing is that D is AC's midpoint And BD is the median of triangle Now this vortex which we have started with B vortex can be done with any vortex For example, again same figure is written Let's name it A, B, C Now instead of B, we pass the median from A So if I go like this Now this D is B, C's It is the midpoint. AD is the median. Similarly, now we will make the median from point C. So, let's name it ABC. Now, if you are passing a line from this C point, the line has slanted a little. So, let's suppose we are passing from here and it is going to its midpoint. So, AB's midpoint is D. So, now... So, C D is the median. So, here B D is the median. Here A D is the median. And here C D. Okay. So, that line should go through vortex. And the opposite side of the line should be touched at the midpoint. So, that is the median of triangle. Okay. Let's come to the next topic. Now, the next topic is attitude. So, what is attitude of triangle? What is the attitude of triangle? If we go by definition, it means a line which passes through a vertex and is perpendicular on the opposite side Perpendicular means a straight line that forms an angle of 90 degree So again we make a triangle Let's suppose this is a triangle. This is a triangle ABC. Now a line is going straight from A which is making perpendicular on BC. A is a vertex and BC is opposite side. Here also it is making perpendicular. So AD is our... Now you will think what is the difference between median and altitude? Median is also like this but the difference is that in median this D is the midpoint of BC When it is a line vortex it meets at the midpoint But in case of altitude it is perpendicular Now see here you might find median but if I take a triangle like this Now this is my triangle okay and again this is A, B, C Now I am making an appendicular line from A like this So I am saying that my attitude is AD Now this D is not the midpoint of BC We can clearly see that if it is BC then its midpoint will be somewhere here Right? So, the line which goes like this, this will be your median Because it is coming at the midpoint But it is perpendicular So, it is perpendicular means it is altitude Again, as the median can be made with any vortex Similarly, your altitude can also be made with any vortex If you make it with C, then it is perpendicular to AB If you make it with B, then it is perpendicular to AC So, this is altitude of triangle. Okay, let's come to the next topic. So our next topic is exterior angles of triangle and its properties. So now we will discuss exterior angle and then its properties. So the first thing is exterior angle what is it? So if I draw this triangle and here I say angles remember this is angle 1, this is angle 2, this is angle 3, this is angle now angle 1,2,3 are interior angles of triangle because they are inside the triangle If I extend it from here, then the angle which will be formed here, you can see this is an angle. So this angle will be exterior angle because it is formed outside the triangle. And it is not necessary that it can be formed only here, it can be formed from any vortex. If you extend it from here, then it will be like this, if you extend it from below, then it will be like this, if you extend it from above, then it will be formed here. So means there are many exterior angles to a triangle. Now we understood what is exterior angle. Now let's come to its property. So exterior angle's property is, if we see its definition then it is an exterior angle is equal to the sum of two interior opposite angles. Now let's break this definition and understand. So an exterior angle, let's suppose let's take this and let's name it 4. So an exterior angle is equal to exterior angle equal to sum of two opposite interior angles sum of two, two angles, interior angle opposite now what is the meaning of opposite? if you are taking this, then angle 3 will not be included opposite of this angle 1 and angle 2 3 not included so this means property according angle 4 which is exterior angle will be equal to Sum of angle 1 and angle 2. Why angle 1 and 2? Because it is interior angle and opposite angle. So, 3 is not included. So, according to this property, the angle outside is equal to the sum of opposite 2 angles inside. Okay. So, how can we get questions based on this? Let's discuss that. So, I am drawing a figure here. Let's suppose you are given this triangle. Okay? And in that you are given that this angle is of 50 degree and this angle is of 60 degree. I am taking imaginary measures. So, don't go into depth that this triangle will not be like this but it will be like this. So, these are just imaginary measures. You are given that one angle is 50 and other is 60. Find X. Now, you have to find X. Find it. Now angle X is the exterior angle. So, according to exterior angle property, angle X will be equal to 50 degree plus 60 degree. Right? The sum of these two will be equal. So, 50 plus 60 is 110 degree. Okay? So, you have to find the outer angle. Next, there can be one more thing. That can be... Same, we have made a triangle here. And here you are given this. Let's suppose it is given 110 degree. And then you are given this 70 degree. You have to find this angle which is interior. Now exterior is given, interior you have to find. So again 110 degree is equal to 70 plus x. Right or wrong? Because Exterior angle of both will be equal to sum. So, here we have to find x. 70 is plus so it will be minus. So, 110 minus 70 degree equals to x. Now, 11 minus 7 is 4. So, 0. This will become 40 degree. So, means angle x here equals to 40 degree. Okay. So this was about exterior angle and its properties. Let's come to the next topic. Now our next topic is angles and property of triangle. Now what is the angles and property? Angles and property according to the sum of the measures of three angles of a triangle is 180 degree. So again let's break this definition. Let's understand it. So if you have a triangle then what are its interior angles? So interior angles are This one, this one, this one. So, let's name it 1, 2, 3. So, according to angle sum property, angle 1 plus angle 2 plus angle 3 equals to 180 degree. Now, if you have any triangle, any triangle in any shape, their angles will always be 180 degree. Okay? How can you get questions based on this? Let's suppose you are given two angles This is 60 degree and this is 70 degree Now find this angle Okay You can get questions like this that you have to find this angle So if you have two angles then you can find the third angle Because you know that the sum of all three angles is 180 degree Okay So this is the angles and properties You will get many questions based on this But they are very simple Okay So let's come to the next topic. Now our next topic is types of triangle. See there are many type of triangle but abhi hum wohi discuss karenge jo aapki textbook mein hai aur jo ki aapko required hude. So there are two type of triangle discussed. The first one is equilateral triangle. Aap equilateral triangle kya hota hai? Equilateral triangle mein all sides are equal. Equal to triangle means all the three sides of triangle are equal. Similarly, there is one more property that all the angles are equal. Now, we will discuss one more thing related to all the angles being equal. But before that, let's suppose this is a triangle and all its sides are equal. Let's say, if triangle is A, B, C. So AB equals to BC equals to AC. All three sides are equal. Now let's talk about angles. Now if I say that all three angles of one triangle are equal. So if all three angles are equal, then it can only be in one case. If all three angles are 60 degree. Why? Why did it happen that if all three angles are 60 degree, then also all three can be equal? Because we know the sum of all three angles according to angles and properties. In any triangle, the sum of three angles is 180 degrees If any angle is less than 60 degrees Then we have to change it If one angle is 50 degrees Then the other angle is 70 degrees And then it will be like this that the sum of all three angles is 180 degrees So if you want to keep the sum of all three angles as 180 degrees Then all three triangles will be 60 degrees Only then it is possible Okay So this was about equilateral triangle What did we learn in equilateral triangle? We know that z equals Tino angles equal or we can say tino ka measure 60 degree. Okay. So, this was about equilateral triangle, the first type of triangle. Let's come to the second triangle. Now, the second type of triangle is isosceles triangle. So, What happens in isosceles triangles? Any triangle has two sides equal. So, two sides are equal. Now what can we conclude from this? Let's suppose this is a triangle. So in this triangle, this side is equal to this side. So it is an isosceles triangle. Similarly, this side can be equal to this side. Again it is an isosceles triangle. Also, this side can be equal to this side. So this means if any of these two sides are equal, then that is an isosceles triangle. Now let's come to the next topic. Now we will discuss the property of triangle. Now a triangle has a property which is based on its sides. Now in this property, if you have any triangle, the sum of any triangle's two sides will always be greater than the third side. Let's understand it. Let's suppose this is a triangle. Let's name it ABC. So according to triangle property, any sum of any two sides i.e. AB plus BC will always be greater than the sum of the third side. So if you add AB and BC, it will always be greater than AC. Similarly, if you add AB and AC, it will always be greater than BC. Similarly, if we take the remaining two sides, then any sum of two sides will always be greater than the third side. Now you might be thinking that it is obvious, it will be like this only. But if we see, where you might get confused, if we have this triangle, suppose we have this triangle. So you will think that this is a small side, we will sum it with this, how will it be greater than this? But as such, It doesn't happen. No matter what the length of this is, if you are adding this and this, these two, then it will be bigger than this side. So, you have to remember this. If someone has given you measurements that these three sides are this and the sum of two sides is smaller than this, then that triangle cannot be made. Okay? So, this is a property which says that sum of any two sides of a triangle is always greater than the third side. Okay, now let's come to the next topic. So, our next topic is right angle triangle and Pythagoras property or theorem. So, Pythagoras theorem bhi bohotay hain, Pythagoras property bhi bohotay hain. But before coming to Pythagoras theorem or property, let's first discuss right angle triangle. So, right angle triangle kya hota hai? Any triangle jiska koi bhi ek angle 90 degree ka ho. For example, this is 90 degree. So if any angle is of 90 degree then it becomes right angled triangle It is not necessary that it can be in any shape It can be like this So here this one is the 90 degree Similarly if it is made like this and this is 90 degree So it can be in many shapes But if angle is of 90 degree then it becomes right angled triangle After this right angle In this triangle, the slanting line where there is 90 degree angle, it has opposite side like this side and this side so this slanting side is called hypotenuse so this is the hypotenuse of the triangle and other than this, the other two sides we call them legs we call it side, base, we give many names and this is the main one This slanting line is the hypotenuse. Now this was about our right angle triangle. One of which is of 90 degree. Now we will talk about the Pythagoras theorem. Now what is the according to Pythagoras theorem? Let's see. So according to Pythagoras theorem, Pythagoras theorem says that if you have any right angle triangle, remember Pythagoras theorem works only where right angle triangle is there. So if you have a right angle triangle, then according to Pythagoras theorem, its hypotenuse is this one. So hypotenuse square is equal to sum of two sides of square. Let me explain it in writing, it will be more clear. So this is PQR. So, according to Pythagoras theorem, P R will be equal to PQK square plus QRK square. means the square of the hyperbolic is equal to the sum of the squares of the other two sides now how can we get the questions here let's suppose you have to find two of these let's take a simple example let's suppose you are given that QR is 12 cm and PQ is 5 cm now you have to find PR so how will you find it let's suppose I take it as X So, this will be x square equals to PQ. PQ is 5 cm. Means 5 square plus QR. QR is 12. So, 12 square. Now, x square equals to 5 square. 5 into 5 is 25. Plus 12 square. 12 into 12 is 144. So, this is 25 plus 144 Now if we add this we will get 169 Now this 169 is not the value of x This is the value of x square Means x square is 169 Now see we have to find the square of 169 So 169 square is 13 So x square equals to I can write 13 square because 169 is 13 Square is there. So, square to square cancel. X will be 13. So, this means X will be equal to 13 cm. Okay. So, this was our Pythagoras theorem. This was the last topic for this chapter. I hope you have understood all these concepts. And when you will do the exercise equations, you will almost know them. Okay. So that's it for this chapter. I'll be coming back again with a new chapter. Till then take care and bye-bye.

Now, the chapter's name is Triangle and its Properties. On properties, first we will know what is triangle. Triangle we all know. It is a closed figure or a closed curve which has three line segments.

So this can be a triangle. Similarly this can be a triangle. So there are many shapes of a triangle which is possible.

So if three line segments are joining then that is a triangle. Also it is a closed figure. Okay.

Now here also there are some parts of triangle. Like first of all let's talk about side. Let's take this triangle.

Let's name it PQR. Now what are the sides of this triangle? PQ is the side.

Sides are its line segments. So PQ. Similarly QR. Then we have PR.

So these are the sides of the triangle. Next is angles. Now in triangles we have angles.

Angles are Angle P, angle Q, angle R. So if I write angle P, it can be written as angle Q, P, R. Or angle R, P, Q, making sure that P comes in between. Similarly, angle P, angle Q, angle R.

Okay, so these are angles of triangle. Next we have The vertices of triangle. Now what are vertices?

You must have read vertex. So vertex are corner points. Like in this triangle, this is the corner point, this is the corner point and this is the corner point.

So these corner points are vertex of triangle or we can say vertices of triangle. So the vertices are P, Q, R. Right? These are the vertices of triangle. Okay, so this was a short introduction about what are triangles Now let's come to some more topics and concepts which will be discussed in this chapter So the next topic is Median So we will discuss what is Median of Triangle What is the Median of Triangle? When a line connects any vortex of a triangle with the midpoint of its opposite side Now it must be very confusing, let's understand it with a figure So here is a triangle Now any of its vortexes, where is the vortex?

This is the vortex, this is the vortex and this is the vortex So a line which starts with a vortex, let's suppose we are starting with this vortex So it will pass through from here and the opposite side of this vortex is this At its midpoint, so this is triangle AB C and this cone is point D So the biggest thing is that D is AC's midpoint And BD is the median of triangle Now this vortex which we have started with B vortex can be done with any vortex For example, again same figure is written Let's name it A, B, C Now instead of B, we pass the median from A So if I go like this Now this D is B, C's It is the midpoint. AD is the median. Similarly, now we will make the median from point C. So, let's name it ABC. Now, if you are passing a line from this C point, the line has slanted a little.

So, let's suppose we are passing from here and it is going to its midpoint. So, AB's midpoint is D. So, now...

So, C D is the median. So, here B D is the median. Here A D is the median.

And here C D. Okay. So, that line should go through vortex. And the opposite side of the line should be touched at the midpoint. So, that is the median of triangle. Okay.

Let's come to the next topic. Now, the next topic is attitude. So, what is attitude of triangle? What is the attitude of triangle? If we go by definition, it means a line which passes through a vertex and is perpendicular on the opposite side Perpendicular means a straight line that forms an angle of 90 degree So again we make a triangle Let's suppose this is a triangle.

This is a triangle ABC. Now a line is going straight from A which is making perpendicular on BC. A is a vertex and BC is opposite side.

Here also it is making perpendicular. So AD is our... Now you will think what is the difference between median and altitude?

Median is also like this but the difference is that in median this D is the midpoint of BC When it is a line vortex it meets at the midpoint But in case of altitude it is perpendicular Now see here you might find median but if I take a triangle like this Now this is my triangle okay and again this is A, B, C Now I am making an appendicular line from A like this So I am saying that my attitude is AD Now this D is not the midpoint of BC We can clearly see that if it is BC then its midpoint will be somewhere here Right? So, the line which goes like this, this will be your median Because it is coming at the midpoint But it is perpendicular So, it is perpendicular means it is altitude Again, as the median can be made with any vortex Similarly, your altitude can also be made with any vortex If you make it with C, then it is perpendicular to AB If you make it with B, then it is perpendicular to AC So, this is altitude of triangle. Okay, let's come to the next topic.

So our next topic is exterior angles of triangle and its properties. So now we will discuss exterior angle and then its properties. So the first thing is exterior angle what is it? So if I draw this triangle and here I say angles remember this is angle 1, this is angle 2, this is angle 3, this is angle now angle 1,2,3 are interior angles of triangle because they are inside the triangle If I extend it from here, then the angle which will be formed here, you can see this is an angle.

So this angle will be exterior angle because it is formed outside the triangle. And it is not necessary that it can be formed only here, it can be formed from any vortex. If you extend it from here, then it will be like this, if you extend it from below, then it will be like this, if you extend it from above, then it will be formed here.

So means there are many exterior angles to a triangle. Now we understood what is exterior angle. Now let's come to its property. So exterior angle's property is, if we see its definition then it is an exterior angle is equal to the sum of two interior opposite angles.

Now let's break this definition and understand. So an exterior angle, let's suppose let's take this and let's name it 4. So an exterior angle is equal to exterior angle equal to sum of two opposite interior angles sum of two, two angles, interior angle opposite now what is the meaning of opposite? if you are taking this, then angle 3 will not be included opposite of this angle 1 and angle 2 3 not included so this means property according angle 4 which is exterior angle will be equal to Sum of angle 1 and angle 2. Why angle 1 and 2?

Because it is interior angle and opposite angle. So, 3 is not included. So, according to this property, the angle outside is equal to the sum of opposite 2 angles inside. Okay.

So, how can we get questions based on this? Let's discuss that. So, I am drawing a figure here. Let's suppose you are given this triangle. Okay?

And in that you are given that this angle is of 50 degree and this angle is of 60 degree. I am taking imaginary measures. So, don't go into depth that this triangle will not be like this but it will be like this. So, these are just imaginary measures. You are given that one angle is 50 and other is 60. Find X. Now, you have to find X.

Find it. Now angle X is the exterior angle. So, according to exterior angle property, angle X will be equal to 50 degree plus 60 degree.

Right? The sum of these two will be equal. So, 50 plus 60 is 110 degree.

Okay? So, you have to find the outer angle. Next, there can be one more thing.

That can be... Same, we have made a triangle here. And here you are given this. Let's suppose it is given 110 degree.

And then you are given this 70 degree. You have to find this angle which is interior. Now exterior is given, interior you have to find.

So again 110 degree is equal to 70 plus x. Right or wrong? Because Exterior angle of both will be equal to sum.

So, here we have to find x. 70 is plus so it will be minus. So, 110 minus 70 degree equals to x.

Now, 11 minus 7 is 4. So, 0. This will become 40 degree. So, means angle x here equals to 40 degree. Okay. So this was about exterior angle and its properties. Let's come to the next topic.

Now our next topic is angles and property of triangle. Now what is the angles and property? Angles and property according to the sum of the measures of three angles of a triangle is 180 degree. So again let's break this definition.

Let's understand it. So if you have a triangle then what are its interior angles? So interior angles are This one, this one, this one.

So, let's name it 1, 2, 3. So, according to angle sum property, angle 1 plus angle 2 plus angle 3 equals to 180 degree. Now, if you have any triangle, any triangle in any shape, their angles will always be 180 degree. Okay?

How can you get questions based on this? Let's suppose you are given two angles This is 60 degree and this is 70 degree Now find this angle Okay You can get questions like this that you have to find this angle So if you have two angles then you can find the third angle Because you know that the sum of all three angles is 180 degree Okay So this is the angles and properties You will get many questions based on this But they are very simple Okay So let's come to the next topic. Now our next topic is types of triangle.

See there are many type of triangle but abhi hum wohi discuss karenge jo aapki textbook mein hai aur jo ki aapko required hude. So there are two type of triangle discussed. The first one is equilateral triangle.

Aap equilateral triangle kya hota hai? Equilateral triangle mein all sides are equal. Equal to triangle means all the three sides of triangle are equal. Similarly, there is one more property that all the angles are equal.

Now, we will discuss one more thing related to all the angles being equal. But before that, let's suppose this is a triangle and all its sides are equal. Let's say, if triangle is A, B, C. So AB equals to BC equals to AC.

All three sides are equal. Now let's talk about angles. Now if I say that all three angles of one triangle are equal. So if all three angles are equal, then it can only be in one case. If all three angles are 60 degree.

Why? Why did it happen that if all three angles are 60 degree, then also all three can be equal? Because we know the sum of all three angles according to angles and properties. In any triangle, the sum of three angles is 180 degrees If any angle is less than 60 degrees Then we have to change it If one angle is 50 degrees Then the other angle is 70 degrees And then it will be like this that the sum of all three angles is 180 degrees So if you want to keep the sum of all three angles as 180 degrees Then all three triangles will be 60 degrees Only then it is possible Okay So this was about equilateral triangle What did we learn in equilateral triangle?

We know that z equals Tino angles equal or we can say tino ka measure 60 degree. Okay. So, this was about equilateral triangle, the first type of triangle.

Let's come to the second triangle. Now, the second type of triangle is isosceles triangle. So, What happens in isosceles triangles?

Any triangle has two sides equal. So, two sides are equal. Now what can we conclude from this?

Let's suppose this is a triangle. So in this triangle, this side is equal to this side. So it is an isosceles triangle.

Similarly, this side can be equal to this side. Again it is an isosceles triangle. Also, this side can be equal to this side.

So this means if any of these two sides are equal, then that is an isosceles triangle. Now let's come to the next topic. Now we will discuss the property of triangle. Now a triangle has a property which is based on its sides.

Now in this property, if you have any triangle, the sum of any triangle's two sides will always be greater than the third side. Let's understand it. Let's suppose this is a triangle. Let's name it ABC. So according to triangle property, any sum of any two sides i.e.

AB plus BC will always be greater than the sum of the third side. So if you add AB and BC, it will always be greater than AC. Similarly, if you add AB and AC, it will always be greater than BC. Similarly, if we take the remaining two sides, then any sum of two sides will always be greater than the third side. Now you might be thinking that it is obvious, it will be like this only.

But if we see, where you might get confused, if we have this triangle, suppose we have this triangle. So you will think that this is a small side, we will sum it with this, how will it be greater than this? But as such, It doesn't happen. No matter what the length of this is, if you are adding this and this, these two, then it will be bigger than this side. So, you have to remember this.

If someone has given you measurements that these three sides are this and the sum of two sides is smaller than this, then that triangle cannot be made. Okay? So, this is a property which says that sum of any two sides of a triangle is always greater than the third side.

Okay, now let's come to the next topic. So, our next topic is right angle triangle and Pythagoras property or theorem. So, Pythagoras theorem bhi bohotay hain, Pythagoras property bhi bohotay hain.

But before coming to Pythagoras theorem or property, let's first discuss right angle triangle. So, right angle triangle kya hota hai? Any triangle jiska koi bhi ek angle 90 degree ka ho.

For example, this is 90 degree. So if any angle is of 90 degree then it becomes right angled triangle It is not necessary that it can be in any shape It can be like this So here this one is the 90 degree Similarly if it is made like this and this is 90 degree So it can be in many shapes But if angle is of 90 degree then it becomes right angled triangle After this right angle In this triangle, the slanting line where there is 90 degree angle, it has opposite side like this side and this side so this slanting side is called hypotenuse so this is the hypotenuse of the triangle and other than this, the other two sides we call them legs we call it side, base, we give many names and this is the main one This slanting line is the hypotenuse. Now this was about our right angle triangle.

One of which is of 90 degree. Now we will talk about the Pythagoras theorem. Now what is the according to Pythagoras theorem?

Let's see. So according to Pythagoras theorem, Pythagoras theorem says that if you have any right angle triangle, remember Pythagoras theorem works only where right angle triangle is there. So if you have a right angle triangle, then according to Pythagoras theorem, its hypotenuse is this one. So hypotenuse square is equal to sum of two sides of square. Let me explain it in writing, it will be more clear.

So this is PQR. So, according to Pythagoras theorem, P R will be equal to PQK square plus QRK square. means the square of the hyperbolic is equal to the sum of the squares of the other two sides now how can we get the questions here let's suppose you have to find two of these let's take a simple example let's suppose you are given that QR is 12 cm and PQ is 5 cm now you have to find PR so how will you find it let's suppose I take it as X So, this will be x square equals to PQ. PQ is 5 cm. Means 5 square plus QR.

QR is 12. So, 12 square. Now, x square equals to 5 square. 5 into 5 is 25. Plus 12 square.

12 into 12 is 144. So, this is 25 plus 144 Now if we add this we will get 169 Now this 169 is not the value of x This is the value of x square Means x square is 169 Now see we have to find the square of 169 So 169 square is 13 So x square equals to I can write 13 square because 169 is 13 Square is there. So, square to square cancel. X will be 13. So, this means X will be equal to 13 cm. Okay. So, this was our Pythagoras theorem.

This was the last topic for this chapter. I hope you have understood all these concepts. And when you will do the exercise equations, you will almost know them.

Okay. So that's it for this chapter. I'll be coming back again with a new chapter.

Till then take care and bye-bye.

Transcript for:Understanding Triangle Properties and Types

Transcript for:
Understanding Triangle Properties and Types