Math Isip · Transcript · · Updated
Grade 8 MATH Term 2 Week 3: Pythagorean Theorem & Its Converse | MATATAG - 2nd Term/Quarter Tagalog – Transcript
Video by Math Isip · Watch the original on YouTube
Summary
AI-generated from the transcript. Verify details against the source video.
- The Pythagorean theorem states that for any right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.
- Pythagorean theorem is used in finding the missing side of a right triangle.
- The converse of the Pythagorean theorem is used to classify triangles by sides as acute, right, or obtuse.
Use this video with Pro
Reading, copying and transcript downloads are free. Create saved AI results for this video with a signed-in Pro account ($9/month).
Transcript
Search ignores accents. All transcript text stays visible.
[Musika] Hello everyone. Welcome ulit sa ating Matthisip YouTube channel where you can find free Tagalog Mathematics tutorial.
Our topic for today is all about Pythagorean theorem and its converse. But before we begin, let me just thank everyone for supporting our channels. Maraming salamat po for uh watching and clicking and subscribing to our channel.
And to our fellow teachers, thank you very much for sharing this to our dear learners. And by the way, if you are interested with our PowerPoint presentations, we offer this product, just send us a message on our Facebook page. The link is in the description below. Okay. So without further ado, let's now begin with our lesson.
Okay. The learning competency for today is to apply the Pythagorean theorem in finding the missing side of a right triangle and it's converse in classifying triangles. All right. So let's start with this engagement activity. Think about this. A new flat screen TV has a width of 40 in and a height of 30 in. Okay. As you can see here in this illustration we have 30 in
by 40 in. Okay. However, the box label says that TV is 50 in. Okay. 50 in TV. Now, uh is the label correct? What do you think? Ang dimensions niya is 40x 30 but the label says it's 50 in. So saan po nanggagaling yung label natin when it comes to the measurement of television.
All right. So actually if we measure the diagonal of this television that's where we know if this is really a correct label. Okay? So paano po natin yan gagawin if we don't have a measuring tool? For example, we just rely it on the uh measurement given here in the wid height. Paano natin siya malalaman without using any measuring tool? Okay.
So we have actually a way for that. By the way, what kind of triangle is this? What triangle are we dealing with? And we will answer the question, how can we find the length of a diagonal or missing side if we only know the other two sides? Okay, these questions will be answered by our lesson for today.
Okay, to answer the first question, what kind of triangle is this? This is what we call a right triangle. Remember, a right triangle is a triangle with one angle equal to 90°. And we often use a box in order for us to indicate that this is 90°.
And how do we call the sides? We have what we call the hypotenuse. This is the side opposite the right angle. Uh this is the hypotenuse and it is the longest side. And how do we call the other two sides? We call them legs. All right? In a right triangle, they are called legs.
The two sides forming the right angle. So these are the two legs. Okay. Now for the next question, how do we measure the longest side of a right triangle given the two legs? We now have what we call the Pythagorean theorem or the Pythagorean theorem. Now, for any right triangle, ang ibig sabihin ng Pythagorean theorem is for any right triangle, the sum of the square of the
lens of the legs equals the square of the length of the hypotenuse. All right. So kung niyo maintindihan yung definition niya, we just make use of our equation. This is the Pythorean theorem equation. Okay, as you can see, we have here a squ + b s is equ c s. Now what are these variables? We can say that A and B are
the legs and C is the hypotenuse. All right. So again A and B itong legs na ito A and B and then the hypotenuse is letter C. So if we're going to add the square of A and the square of B, it will be equal to the square of the longest side or the hypotenuse. Yun lang po ang ibig sabihin ng Pythagorean theorem.
Okay. Now, anong gamit ng Pythagorean theorem? Now, Pythagorean theorem is used in finding the missing side of a right triangle. So, how do we do that? Let's have this examples. All right, let's have example number one basing from our engagement activity kanina, the television which is uh has 40 in uh width and then 30 in height. So find the hypotenuse of a
right triangle with legs 40 in and 30 in. So first let's label our triangle. Iung kanyang legs we have A. Usually ang A is iyung horizontal and then yung B natin is iyung vertical. But actually it can be ah pwede namang interchangeable iyan. So we have here B is equ to 30 in.
Now we are looking for the hypotenuse or yung C. So using our pythagorean theorem which is a s + b s equ c s all we have to do is to substitute yung mga given.
So we have here a s which is 40. You get the square of 40. Next we have b squ which is b is 30. Get the square. So we have 30 s is equal to c s. Given ba ang c? Hindi. Siya po yung hinahanap natin.
So we have here c squ. Now we can actually interchange this in an equation. Remember the properties of equality where we can say that C s is equ to 40 s + 30 s because we use the symmetric property of equality.
Binaliktad lang po natin sila since we are we are trying to solve C ano yung value ng C. Kaya yung C yung nandito sa left side and then yung mga ibang terms nasa right side. Nilipat lang po natin sila. Flinip lang natin sila kumbaga.
Alr. So we have here 40 s. We just simplify this. So 40 s means 40 * 40 we get 1,600. And then 30 s means 30 * 30 we get 900.
Now we can add this 100 1,600 + 900 it will be 2,500. Now do we have a value for C? Ah you might say yes but no. We have here C squ. Hindi po yan yung hinahanap natin.
C. Wala dapat siyang square. So anong gagawin natin para makuha lang natin si square? Al right. I mean si C not the square. So what we can do here is to uh do the opposite of squaring which is to get the square root. Okay? Pag kinuha mo yung square root ng c s makukuha mo si C. So dito ganun din ang gagawin natin sa kabilang side. Whatever we do on one side of the equation ganun din po ang
gagawin natin si sa other side of the equation. So we have here instead of 2,500 we just get the square root of 2,500. Therefore magiging C na lang ito. Okay? And then this one we just get the square root of 2,500 and we will get 50. All right.
Therefore, the value of C is equal to 50. Thength of the hypotenuse is 50 in. So this is 50 in. Okay. So, going back to our engagement activity kanina sa introduction, the question is asking, "Is the label correct? Is this really a 50 in TV?" Well, the answer is yes.
Because using the Pythagorean theorem, we were able to find the measurement of the diagonal using the given width and then the height. All right. So, yun po ang gamit ng Pythagorean theorem.
Okay, let's have another example. Example number two. Okay, let me read the problem. A rescue worker places a 13 m ladder against a building. The foot of the ladder is 5 m from the wall. How high up the wall does the ladder reach?
All right. So, given this illustration, okay, let's just label kung ano iyung mga measurement nung ating triangle. First, nasan ba diyan yyung triangle natin? Okay, yes, this is our triangle. As you can see, this is a right triangle. Okay, remember this is a building. So dapat uh 90 degrees po yung tayo niya no'no. So let's have the first given 13 m yung ating ladder. So our
hypotenuse here is the ladder. Therefore it is 13 m. C is equ 13 m. Next is the foot of the ladder is 5 m from the wall. Meaning from this wall going to the ladder the foot of the ladder it is 5 m.
So this will serve as our one of our leg which is a. Okay. A is equ to 5 m. Now, how high up the wall does the ladder reach? Ito na po 'yung hinahanap natin. Gaano kahaba itong side na 'to? So this is our leg B. So it is unknown. All right. So how do we solve for this? We can also use the Pythagorean theorem.
Now, if you are asking bakit naman iyung hypotenuse iyung hinahanap dito but yes we can still use this because there's only one side missing. Okay, we can still use the Pythagorean theorem. So how? Okay, let me show you the solution. So first let us substitute. A squ 5 s. Our a is 5. B s is unknown. That's why hindi muna natin
siya masa-substitute. And then C squ C is known which is 13 m. So let's just get the square of 13. Now we have here B squ. Yun po yung sino-solve natin. So it's important that this will be separated on one side of the equation.