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Grade 8 MATH Term 2 Week 3: Triangle Inequality Theorems | MATATAG - 2nd Term/Quarter Tagalog – Transcript
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Summary
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- The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
- The corolary of the triangle inequality states that the length of any side of the triangle is greater than the difference of the other two sides.
- According to the angle side relationship theorem, the longer side in a triangle is opposite the larger angle and the shorter side is opposite the smaller angle.
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[Musika] Hello everyone. Welcome po ulit sa ating Mattisip YouTube channel where you can find free Tagalog Mathematics tutorial. Our topic for today is all about triangle inequality theorems and their corolaries. But before we begin, let me just thank everyone for supporting our YouTube channel. And if you haven't subscribed to our channel yet, we
encourage you to click the subscribe button to support us with our free Tagalog mathematics tutorial for those who want to learn more about mathematics. And for our teachers, I would like to thank you for sharing this to our dear students. And teachers, if you want to avail of our PowerPoint presentation so that you can use it in your lessons, you can contact us on our Facebook page. All right. So without further ado, let us now begin with our lesson.
All right, at the end of the lesson, you will be able to apply the triangle inequality theorems to establish results for angles and sides in triangles. All right, but before we begin, let's have this questions for you to think about first. All right. So we have here can we make a triangle with these three drinking straws? Let's say for example you have this 4 cm straw, 6 cm and then
10 cm straw. Makabuo ba tayo ng isang triangle out of these three straws? What do you think? Okay, to do that, we can actually move this straws and then let's form a triangle. Let's see. Okay. Tignan natin kung magiging triangle siya. All right. So, if you take a look at this, do you think this is a triangle?
Well, there is an opening. Hindi natin kayang pagdikitin yan kahit na i-move pa natin siya. So, this is not possible. 4 cm, 5 cm, and 10 cm straws can't make a triangle.
So the question is without moving the straws, how can we tell when three lens form a triangle? Paano natin malalaman without moving the straws, okay? With just the measurement, paano natin malalaman kung makakabuo tayo ng triangle? Let's say there are other measurements. Paano natin malalaman iyon? And another question is how do the angles and sides of a triangle compare
with one another? Okay, so these questions will be answered through our lesson for today. Okay. So the answer for those question the first question is what we call the triangle inequality theorem and its corolary. So what is this? Let's take a look. First let's have the definition of this theorem. Okay. What is triangle inequality theorem? In any triangle, the
sum of the lens of any two sides of a triangle is greater than the lens of the third side. So let's visualize it using this triangle. So any kind of triangle naman ano in this case this is an scaline a scaline triangle. Remember scaline triangle has different uh sides measurements of the sides. Okay. So let's say the sum of the length of any
two sides we have here side A, side B and then side C okay is greater than the length of the third side. So for example we have here the first two side a + b. A + B. 'ag pinag-add natin 'yan, 'ag pinag-combine natin 'yan, the sum is always greater than the third side, which is side C.
Okay, do you agree? All right, good. Next, what if we add side B and side Can, so we have here side B plus side C. Pag pinag-add ba natin to, is it greater than side A? Of course. Okay. Next. How about side A and side C? So, how about this two sides? Side C and then side A.
Okay. Obviously ag pinagdugtong natin yan, it is always uh longer than the third side which is in this case side B na yung third side natin. So yun po yung ibig sabihin ng triangle inequality theorem. Okay? You pick any two sides pag pinag-combine mo, it is always greater than the third side.
Okay. Now to apply this para masagot natin yung question natin kanina to know if three sides can form a triangle. Let's have some examples. All right. So let's have number one. Okay. Check if 4 cm, 7 cm and 10 cm can form a triangle.
We have here three sides of a triangle. Let's see if it can really form a triangle. So using the triangle inequality theorem, let's have this sum of two sides. Pag i-add natin yung two sides and then i-compare natin siya sa third side. So let's have the first two sides. Ang gagamitin natin ngayon is yyung 4 tsaka seven muna. If we're going to add 4 and 7, the answer is 11. Now let's compare it with the third side. So
since we have 4 and 7, 4 and seven, ang third side na natin ngayon is yung 10. So the third side is 10. So is it uh greater or lesser? All right, good. The sum of the two sides 11 is greater than 10. So na na-meet niya yyung ating theorem kanina. Now let's have let's pick another two sides aside from 4 and 7. So we have here 7 and 10. A combination of 7 and 10. Pag pinag-add
ba natin yan, mas higit ba siya sa third side? So the third side now will be of course 4. Now 17 yes is greater than 4. So na-meet pa rin niya yung ating inequality theorem. Now let's pick the last combination of sides. So na-pick na natin si 4 and 7. Na-pick na natin si 7 and 10. How about 4 and 10? Okay. So 4 + 10 the answer will be 14. Now 4 and 10.
Ano na ang naiwan? Ito na po yung third side natin. Si seven. So what is or which is greater? Yes, the sum of the two sides is still greater than the third side. So pag na na-meet niya iyung tatlong yan, ibig sabihin that is a triangle. A triangle can be formed using 4 7 and 10 cm.
Okay. Let's have another example. Let's check if 16 cm, 9 cm and 6 cm can form a triangle. Okay, let's start with the first combination. Let's add 16 and 9. These two sides. Will it be greater than 6? Let's see. The third side is 6. Okay.
Yes. 16 + 9 is 25. It is greater than the third side 6. All right. Na-meet niya yung ating theorem. Next, let's pick another two sides. So, we have six and 16 and six naman ngayon. 16 and 6.
Pag pinag-add natin, it will be 22. Is it greater than the third side? For this case, it's 9. Okay. Yes. Greater pa rin po yung add sum ng two sides natin. Now, ano pa yung hindi natin pinag-add sa tatlong to? We can add uh 9 and 6. Okay, let's add 9 and 6. Will it be greater?
The answer is 15. Ano na yung naiwan? Pag pinag-add natin yung 9 and 6, ang naiwan is yung 16. Yun na. Yun na yung third side. So is 15 greater than 16? Oops. Hindi po siya greater. Therefore, hindi niya namet yung ating triangle inequality theorem. Anong ibig sabihin niyan? Pag may hindi na-meet, ibig sabihin it's not greater. Therefore,
triangle cannot be formed. Dapat any combination pwede, no? Hindi pwedeng may isang combination na pag pinag-add mo mas maliit kaysa sa third side. So we cannot form a triangle using 6 16 and 9 cm. All right. Okay. Next let's have example number three.
Okay. This time we are going to go back with our engagement activity kanina. Well, alam na natin iyung sagot dito. We cannot form the triangle using this three straws. But without moving this straws, we can actually do that using this triangle inequality theorem. So, can we make a triangle with this three drinking straws? Let's use triangle inequality theorem. The sum of two
sides, let's pick. Okay, let's pick 10 and then 4 this time. And then the answer will be 14. Pag pinag-add natin, let's compare it with the third side which is now six. Okay, greater. Yes, na-meet naman niya. Now, let's pick another one. How about 10 and 6? 10 + 6 is 16. It's greater than the the third side which is 4. So, pwede pa rin no.
But if we take a look at 4 and 6, pag pinag-add po natin yan, it will now be 10. So, is it greater than the third side, which is also 10? No, they are not. greater or less than it is actually equal.
Therefore, it did not meet pa rin yung ating triangle inequality. It should be greater. No, this should be greater. So, the triangle cannot be formed. Okay. So, ang technique natin dito class is take a look at the smallest uh sides. Yun lagi ang unahin mo para you don't need to undergo these three trials. Kahit ito na inuna mo, 4 + 6, nakita mo 10, it is
equal to the third side which is 10. It's not greater. Ibig sabihin hindi na siya triangle. Okay. So ang technique natin always start with the two smallest or least measurement then yun yung i-add mo para makita mo kung greater siya doon sa third side natin. Okay? All right. So let's see. Let's practice this using this exercise. You can do this on a paper. Try to do this first. You can
pause this video and then try to play later on nasagot mo na so we can guide you with the correct answers. [Musika] [Palakpakan]
[Palakpakan] Okay, I hope you are now ready and I hope tinay mong sagutan to because remember in order for us to learn is we have to practice. Okay? We cannot learn mathematics if we do not do mathematics.
Okay? So let's take a look at the solution. First we have here the lens 9, 11 and 12 cm. Okay? Sabi ko nga sa inyo, unahin niyo 'yung pinakamaliit na dalawang pinakamaliit na sites which is here in this case is 9 and then 11.
I-add mo na siya kaagad. So 9 and 11 is it greater than the third side which is 12. 9 + 11 is 20 and then greater siya kay 12. So the answer is yes. Okay. Next one. We have here 5 and 8. I-add mo na kaagad si 5 and 8. The answer will be 13. It's not greater than the third side 15. It's less than. Therefore, the answer is no. Okay. Next we have here 5