Grade 9 MATH Term 1 Week 9: Solving Problems Involving Parallelograms | MATATAG Quarter 2 Tagalog

0:07 [bell] Hello everyone. Welcome ulit sa ating Matt is Eisip YouTube channel where you can find free Tagalog Mathematics tutorial. Our topic for today is all about solving problems involving parallelograms rectangles squares and rombuses. Ito po ang lesson natin for grade 9 week number 9. Okay. But before we begin, let me just remind everyone para po masuportahan niyo ang ating channel at maipagpatuloy natin ang mga lessons natin, please subscribe to our channel and also you can follow us on our Facebook page. Especially to our dear teachers who would like to uh avail of our presentations, you can message us on our Facebook page. Okay. So without further ado, let's now begin with our lesson.

0:55 Dito po sa ating lesson, tuturuan ko po kayo kung paano po mag-solve ng problems involving parallelograms and not only parallelograms, but also the special parallelograms like rectangles, squares, and rombuses. Okay, i-apply po natin yung mga properties of these parallelograms. Okay, so let's begin with this question. Can we determine the missing side angle or diagonal without measuring it directly? Like for example, the windows, okay? Yung mga signages natin, street signs, yung mga tiles and then yung mga panels natin. If they are a parallelogram, can we determine iyung mga sides, angles or diagonals without even using our measuring tools? Okay, let's find out later gamit iyung mga

1:42 properties. Okay, speaking of properties, let's review property of a parallelogram. Okay, so first, by definition, ito po ang ibig sabihin ng parallelogram. Opposite sides are parallel. So, as you can see, we have here this uh left and right side. Parallel sila. And then itong nasa taas and then itong nasa baba they are also parallel. Next, aside from that, opposite sides are also congruent. Okay? So, these two sides are congruent. Itong nandito sa taas and baba congruent as well. And then we also have here opposite angles are congruent. So this angle is opposite to this angle they are congruent and this angle is opposite to this angle they are equal as well. And

2:27 then next consecutive angles are supplementary. Meaning to say if we have here this angle 70° iyung kasunod niyang angle dito this is also um 110°. If you add them together, it will be 180°. Ganun din po dito. So if you have your 110, yung kasunod niyang angle dito is 70. If you add them, it will be 180. Therefore, they are supplementary angles. And then next, a diagonal divides a parallelogram into two congruent triangles. Okay. So, if we have here a diagonal, it creates two big triangles dito, no? Ito naman isang diagonal dito. It also creates this triangle and then this triangle. Okay?

3:14 And then lastly, diagonals bisect each other. So ibig sabihin ah this diagonal they intersect with this diagonal dito sa point na ito. And ito po yung point na gitna nung diagonal. Okay? So that's why this segment of the diagonal is also equal to this segment. Ganun din dito sa isang diagonal. This segment of the diagonal is equal to the other segment. So half po talaga yan. All right, there you go. Those are the properties of a parallelogram. Okay, next, let's proceed to properties of a rectangle. Okay, ano naman po ang properties ng rectangle? So, remember, a

4:00 rectangle is also a subset of a parallelogram because opposite sides are parallel. Okay? So, parallel itong sides na ito, ito rin po ay parallel. Now what are the distinct features of a rectangle? So again all parallelogram properties are the properties of a rectangle. Next we have here special properties. Ano yung mga special properties ng rectangle? So ang rectangle alam natin it has four right angles. Okay? As you can see they are all 90°. Next diagonals are congruent. Ibig sabihin, if we have here this diagonal, it is equal length with this diagonal. I

4:46 po yung mga properties of a rectangle. Now, let's proceed to the properties of rombus naman po. Okay. So, first property, all parallelogram properties. Ibig sabihin lahat ng mga nabanggit natin kanina sa properties of parallelogram, it is also the property of a rombus. Okay. Now, ano 'yung mga special properties ng rombus? First, we have here all sides are congruent. So, lahat po ng sides na 'yan ay equal measurement, equal in length. Okay? Aside from that, diagonals are perpendicular. So, these two diagonals, uh, they intersect and they create 90° angle. So, they are perpendicular to each other. Unlike doon po sa

5:32 parallelogram, hindi po necessarily na 90°. Okay? Hindi rin po lahat ng sides sa sa parallelogram and rectangle ay equal in measurement. Okay. Next, diagonals bisect opposite angles. Okay. So here if we have this diagonal, ito iyung opposite angle niya. This angle is opposite to this one. So this diagonal uh divides the angle into two equal parts. Okay? So congruent po yang dalawang angle na yan. Ito rin po congruent din po itong dalawa. Okay? Ganun din dito sa isang diagonal. Okay? Itx ibig sabihin it divides the angles into two equal measures. So this angle itong mas maliit na angle parehas po ang sukat dito sa mas maliit na to. Ganun

6:19 din po dito. They are equal. Okay. Now, let's proceed to the properties of a square. Okay. So, dito po properties of both a rectangle and a rombus. So, ito po yung combination. Since a square is both rectangle and also rombost, iyung properties po nila nandito rin sa properties ng square. Okay, let's uh let's identify all of those properties. So a square has una it has four congruent sides. So lahat po ng sides ng square pantay-pantay po iyan parehas ang sukat. Next po ng angles four are right angles. So all of them are 90° just like a rectangle. Next, congruent diagonals. Okay, ibig sabihin

7:06 yung mga diagonals na ito parehas po ang sukat just like a rectangle. Next, perpendicular diagonals. Yung diagonal nila katulad sa rombus kanina, it creates a 90°. Next, diagonals that bisect each other. So, they intersect at the midpoint of the segment. And then lastly, diagonals that bisect opposite angles. Okay? So if this is 90° and the diagonal bisect that 90°, ano po ang sukat ng bawat ah angle na maliliit dito? Okay? They are 45° each. Okay, very good. So those are the properties of a square. Okay. Now, proceed na po tayo sa solving

7:52 problems involving parallelograms, rectangle, squares, and rombuses. Okay. So, first let's have a simple problem solving strategy on this topic. Pwede natin ong gamiting as guide. Okay. So, step one, we can identify the quadrilateral muna. Anong klaseng quadrilateral siya? Is it a parallelogram, rectangle, rombus or square? Then after that, we can now identify what is given and what is asked. Ano ba ang tinatanong sa problem? Ano ba 'yung mga given na pwede nating gamitin? And then number three, we will now choose the appropriate property. So kung na-identify na natin, we can choose the property of this quadrilateral. And then step four, we will write an

8:38 equation. And then step five, we will solve and check our answer. Okay, so these are our guide not strictly na kailangan nating gamitin, but this can serve as our guide for solving. Okay, let's have example number one. Okay, dito sa example number one, let me read first the problem. Uh, carpenter is making a parallelogram shape wooden frame for a decorative wall panel. The length of the top side is represented by 3x + 4 cm while the length of the opposite bottom side is represented by 5x - 10 cm. Now find the value of x and the length of each of these opposite sides. Okay? So first is ano ba yung

9:25 tinutukoy natin dito? Okay nandito na po sa problem. It's a parallelogram. Okay? So we can draw a parallelogram. mag-drawing tayo ng illustrations para mas madali nating ma-solve 'yung problem. Kung ang given is a word problem, we can actually draw an illustration first para mas ma-visualize natin. And then let's find out. Okay, since this is a parallelogram, ano iyung mga given at ano yung tinatanong dito? So first, ang given sabi diyan is the length of the top side is represented by 3x + 4. So yung length nito it's 3x + 4. How about yung nandito sa baba? Okay? It's 5x - 10. Okay. Now, ano ang tinatanong? Find the value of x. Okay.

10:13 Dito sa ating mga expressions and then the length of each of this uh side or 'yung tinatawag nating side length. Okay. Nung dalawa. Okay. So since ang binigay na given ay uh algebraic expression, kailangan nating mag-solve muna. Okay? Isso-solve natin yung variable x. Okay. So in our solution, what property are we going to use? We can use this property. Opposite sides of a parallelogram are congruent. Itong dalawang sides na to parehas po yan. Pantay po yung sukat. Okay? So we will now write the equation. So kung parehas sila, ano po yung gagamitin natin? 3x + 4 is equal correct to 5x - 10. Okay? So equal yang dalawang side na yan. Then we

10:58 can now solve for the missing uh variable which is yung x. Okay? So solve for x. Okay. Una we can uh combine similar terms 3x and then 5x. Yung 5x ilipat natin dito sa left side kaya magiging - 5x using APE or addition property of equality. Yung 4 naman lilipat sa right side kaya naging -4. All right. Now let's combine 3x - 5x. it will give us -2x and then -10 - 4 it will give us -14. We can now divide these two para makuha natin yung value ng x. Divide them by uh -2. Para maging positive po yung ating uh

11:44 variable, we can multiply this by -1. Kaya magiging 2x + ah sorry 2x 14. Okay? Or pwede rin naman idiretso na natin. We can just divide them both by -2. Divide mo rin to ng -2. Kaya magiging x = 7. Okay. Now, itong nakuha nating value ng x gagamitin natin to solve for the side length. Okay? Isa-substitute lang natin dito sa dalawa. Okay? So, let's find the length of the sides. There are two sides. Unahin natin ong nandito sa taas. Itong top side. 3x + 4. Let us substitute the value of x na nakuha natin kanina. So 3 * 7 it will give us 21 + 4 it will give

12:31 us 25. Now ganun din ba ang makukuha natin dito? Is this also 25? Dapat lang no kasi this is parallelogram. Since we know that both sides are congruent. Kung 25 ito, dapat 25 din ito. But let's find out. Check natin para sigurado. So we have here 5x - 10. I-substitute din natin yung nakuha nating value ng x. So we have here 5 * 7. it will give us 35 - 10 it will also give us 25. So parehas lang po. Ibig sabihin mas na-confirm natin na tama yung sagot. Okay? So therefore, the two opposite sides of the wooden frame are 25 cm each. Okay? So 25 cm 25 cm.

13:20 Okay, example number two. Okay, a designer is making a parallelogram shape garden sign. Two consecutive interior angles of the sign measures 3x + 15° and then 2x + 10°. Find the value of x and the measures of the two angles. Okay? So given this word problem, we can again illustrate para mas ma-visualize natin. So since nabanggit dito parallelogram yyung ating problem, we can just draw a parallelogram and then uh of course this is a parallelogram. Next i-label natin yung mga given. So two consecutive interior angles. So interior angles nasa loob. Okay let's have this one muna. Itong nandito let's say this is the 2x + 10° and then ito naman 3x + 15 ito since

14:09 consecutive magkasunod sila. Pwede rin naman na itong 3x + 15 dito no any of them. Okay? Kahit saan naman diyan pwede nating ilagay. Basta ang importante yung dalawang angle ay magkatabi. Okay? They are adjacent or consecutive. Okay. Next we have here x. Yun yung hinahanap natin value of x. and then the measures of the two angles. Okay? So para mas maganda lagyan natin ng label. Let's say this is angle A and this is angle B. Okay. So alam naman natin if they are supplementary, okay? Ano 'yung property na tinutukoy natin dito? Consecutive angles of a parallelogram are

14:54 supplementary. Ibig sabihin, if we add them together, it will give us 180°. Okay? So yun yung gagamitin nating equation. So first, let's have this two angle. Ia-add natin sila. 3x + 15 'yung first angle. And then i-add natin sa second angle 2x + 10 it will give us 180. Okay. Now let's solve for the value of x. Okay? So we can now combine similar terms dito. So first we have 3x + 2x kaya naging 5x yan. 15 + 10 kaya naging 25. And then ililipat natin si 25 dito sa right side. So 180 - 25 it will give us 155. Now we can divide both sides by 5 para

15:42 makuha natin yung value ng x. So 155 / 5 it will give us 31. Okay? So again hindi na natin kailangang idetalye yung ating mga solution when it comes to algebra. Okay? Kasi napag-aralan na natin yan in your previous grade level. Okay? So x here is equ to 31. Now we can find the measures of the two angles by using the value of x doon sa mga angles natin. Okay? So let's find the measures of the angles. Let's start with itong angle A which is 3x + 15. Ito ah the measurement of angle A is equ to 3x + 15. Let us substitute x is 31. So 3 * 31 it will give us 93 + 15. Therefore the

16:29 measurement of angle A is 108. de okay so 108° po ito. Now let's find out yung isang angle. Well, aside from substituting yung value ng x dito sa second angle, pwede na nating makuha ito by just subtracting it from 180. So 180 - 108. Pwede mo n makuha ito. Pero kung gusto niyo, pwede rin naman yung algebra. So again we can substitute. So since the measurement of angle B is 2x + 10 we will substitute the value of X dito. So magiging 2 * x 2 * 31 2 * 31 is 62 + 10 it will give us 72. Okay. Now if you want to check we can actually add

17:16 this two so 108 + 72 dapat ang kalalabasan nito is 180 kasi nga supplementary sila. So what's the answer? Yes, it's 180°. Therefore, the measures of the consecutive angles are 108° and 72°. Okay, so that's how we solve this problem. Okay. Now, let's proceed to example number three. So, we have here the illustration. Wala pong word problem. Ang nakalagay lang diyan is yung mismong ah illustration. And then sabi dito, find X and side AC. Or is this a side or let's see an Ano ba yung AC dito? Okay. So we have here this parallelogram AB

18:03 CD. Paano natin nasabing parallelogram ito? Okay? If you take a look, meron tayong mga symbol or markings diyan. meaning this uh side here is parallel to this one and this side is also parallel to this one. Okay? Remember our lesson on how we guarantee uh parallelogram. Okay? And then yung AC is ito palang diagonal. Okay? As you can see we have here AC diagonal po iyan and then itong isang diagonal is DB. They intersect at point E. Now we will find the measurement of the diagonal. So yung x natin galing dito sa mga expression na yan. So 4x - 3 ibig sabihin itong segment lang na ito. And then ito naman

18:50 2x + 9 itong segment lang na ito. Okay? So let's have our solution for this parallelogram if we are looking for x and then ac. Okay, first solution, let's have the property. Anong property kaya ang gagamitin natin? So, we are dealing with diagonals. Therefore, ito yyung property na kailangan natin. The diagonal of a parallelogram bisect each other. So, they intersect at their midpoints. Okay? So, ibig sabihin parehas po yan. Pantay. Equal. So equation natin is since equal on 4x - 3 itong segment na ito dito sa 2x + 9 it will be 4x - 3 = 2x + 9. We can now solve for the value of x. Okay? So pag

19:37 may equation na pwede na nating i-solve yung x. So 4x - 3 = 2x + 9. Let's combine similar terms. 4x - 2x kasi ililipat mo 'yung 2x doun sa left side kaya 4x - 2x. Kaya magiging 2x na siya. Okay. Next, itong -3 = 9. Okay. Naiwan pa 'yung 9 diyan. Itong -3 ililipat natin din sa right side. So -3 from -3 magiging + 3. Okay. So So pag naging + 3 na yan, 9 + 3 is 12. All right. And then we can now divide both side by 2 para makuha natin yung x. It will be 6. Okay. So our x here is 6. We

20:23 can now find the length of AE. Okay? Bakit AE muna iyung hahanapin natin dito? Kasi we cannot uh we cannot find AC kapag hindi na hindi natin alam yung measurement ng kalahati or itong AE no? So unahin muna natin yung AE. So we only have here 4x - 3. Isu-substitute natin yung x dito. So magiging 4 * 6. Okay? And then 24 - 3 it will give us 21. So ibig sabihin itong segment ae ito lang kalahati it's 21. Ano po ang measurement nung buo? Kung alam nating equal itong AE dito sa EC, anong magiging measurement ng EC? Okay, dapat 21 din.

21:08 No, pero i-try ulit nating i-solve baka mali yung computation natin. So try natin sa EC naman. So we have here 2x + 9. I-substitute natin yung x dito. So magiging 2 6 it will give us 12 + 9 it will give us also 21. So parehas na-confirm yung ating yung solution natin dito. So ibig sabihin kung ito 21, ito rin ay 21. Malalaman na ba natin yung buong diagonal? Yes, we can just combine the two. 21 + 21 or you can even multiply 1 the 21/2. Ang makukuha natin is 42. So the diagonal AC is equ to 42. Okay. So

21:53 that's how we solve this problem. >> [musika] [musika] [bell] >> Let's have example number four. Okay. So we have here uh word problem. Rectangle MATH has diagonals MT and ah. If MT is

22:41 equ 5x + 2 and ah is equ 7x - 10, find X and the length of each diagonal. So wala tayong figure. So tayo yung gagawa ng illustration. So since nandito na yung clue natin, is a rectangle. Okay. And we have here Mh. Okay. Since iyung empty ay 5x + 2. So alam natin na yung mt is yung diagonal, no? If we connect m and then point t, it will be a diagonal. And yung measurement niya is 5x + 2. Itong buong ito is 5x + 2. Okay. So nandito lang iyung label niya pero we know that this is the whole diagonal. Next uh itong ah naman, itong

23:27 isang diagonal ah ang measurement niya is 7x - 10. Ito naman yung label niya. Okay? So nandito yung label niya pero alam natin na ito yung tinutukoy yung buong diagonal ah out from this problem. Now we will find x. Okay? In this rectangle we will find x and the length of each diagonal. So yung diagonal MT ano ang measurement niya? Yung diagonal ah ano din ang measurement niya? Okay. Now let's proceed to the solution. Anong property po ang gagamitin natin dito? Okay so this is now a special property for rectangle. So iyung property diyan is ito. Diagonals of a rectangle are congruent. So unlike the parallelogram

24:13 na hindi congruent sa rectangle parehas na parehas yan. Okay? So equation natin since meron na tayong expression in for both of these diagonals, we can now say that 5x + 2 is equ to 7x - 10. Okay? Pwede na nating i-solve yung x dito. So solve for x combine similar term 5x i-combine natin sa 7x pero syempre lilipat sa left side kaya magiging negative. From positive magiging - 7x. So 5x - 7x. Ito namang 2 lilipat sa right side kaya magiging -2. Okay? So 5x + 7x it will give us -2x. -10 - 2 it will give us -1. We can divide both by -2. Okay? Kaya magiging x

25:00 = 6. Okay, we can now use this value of x to get the measurement of empty at saka ah. Okay? So, find the length of the diagonal empty. Substitute natin. Since the expression for MT is 5x + 2, gawin nating 6 yung x diyan. So, 5 * 6, it will give us 30 + 2. The answer is 32. Okay. Now, anong susunod? Yung ah naman. So alam niyo na kung ano 'yung sagot diyan no'. Ah alam natin na 'yung dalawang diagonal equal 'yan no'. So kung ano 'yung measurement ng empty, 'yun din dapat ang measurement ng ah. Pero para makasiguro tayo, we can still use algebra. I-substitute ulit natin. So

25:46 from our expression 7x - 10, i-substitute natin yung x dito. So magiging 7 * 6 42 - 10. It will also give us 32. So tama lang iyung computation natin. So ah and empty are both 32. Okay. So that's how we solve example number four. Okay. Now let's proceed to the next example. Example number five. Okay. So diagonals of the diagonals of rombos ABCD intersect at E. Suppose AE is equ 6 cm and BE is equ 8 cm. and the measurement of angle DAB is equ 70°.

26:31 Find the length of the side AB and the measure of angle DAE. Okay? So kapag ganito kasi yung problem, parang hindi natin masyadong maintindihan, hindi rin natin masyadong ma-visualize. That's why we need to draw the figure. So ano pong figure ang tinutukoy dito? It's nandito na po sa problem. It's a rombus. So mag-drawing tayo ng rombus. Ano yung mga points na kailangan natin? We have here a point AB CD. Okay. Now, yung ah diagonals daw ng rombus nag-intersect sa E. So meron tayong dalawang diagonal diyan. Yung point of intersection is point E. Okay. Now, suppose AE. Asan ba yung AE natin? Ito AE. Okay. Suppose AE

27:17 is equ to 6 cm. Okay. Label na natin kaagad yan. Next, yung BE naman. So we have here segment B. So ito BE. Okay. It's 8 cm. Okay. Label na rin natin yan. Now the measurement of angle DA is equ to 70°. Okay? So hanapin natin yung angle DA. We have here DAB. Okay? So 70°. Ibig sabihin yung buo yung buong angle dito. Hindi yung maliliit na angles diyan. So lahat yan 70° daw. Okay. You might be wondering, "Sir, bakit naman naging 70 degrees 'yan? Eh, parang ang luwang niyan. Hindi ata acute angle 'yan." Okay lang po 'yan 'no kasi we are just drawing a figure. Hindi naman kailangan eksakto 'yung drawing natin, 'no? Ang importante ma-visualize

28:04 lang natin 'yung position ng mga angles natin. Okay. Next, find the length of side AB. Anong hinahanap? Itong side AB. And then the measure of DAE. Asan iyung DA natin? De. Okay. So itong maliit na angle dito yun yung hinahanap natin. Okay? So ano po ang properties na kakailanganin natin? So ah in this problem dalawa po ang hinahanap. First is yung side and then iyung second is iyung angle dito. So let's start first with the side. Let's find AB. In this we need the property which is the diagonals of arombus are perpendicular. So meaning we have here this perpendicular symbol. Itong box na

28:49 ito means 90°. We know that this diagonal AC is perpendicular to diagonal BD. No kung ganyan po yung case natin, ah if you can see ito meron tayong nabuong triangle no. Itong triangle na ito, maliit na triangle. Hindi po 'yung triangle na-divide ng diagonal 'no? Ito pong triangle na ito nabuo ng dalawang diagonal. Okay? Ito po 'yun. So we can say that triangle AEB again AEB is a right triangle because of this. They are perpendicular no? So kung right triangle yan ano ang pwede nating gamitin para ma-solve natin ong missing

29:35 side? Okay meron naman na po onong side na ito 8 cm. Itong side na ito given din 6 cm. So dito sa triangle na ito, parang ang nawawala or missing na side ng triangle is ito. Yung pinakamahabang side which is when it comes to the right triangle, meron po tayong tawag dito sa longest side. Okay? Correct. This is the hypotenuse of the right triangle. Okay. So ang equation natin gagamitin natin dito yung pinag-aralan niyo last time in your grade 8 level yung Pythagorean theorem na tinatawag natin. Okay? So in order for us to apply Pythagorean theorem, i-label nga muna natin. So we have here in our right triangle, we usually label it using ABC wherein iyung

30:21 C iyung longest sign or iyung hypotenuse. And then iyung A and B, ito naman yyung mga legs ng right triangle. So what is the formula for getting the what is the Pythagorean theorem formula for getting the hypotenuse? Okay, this is the formula. C S A² + B S. Okay, I believe na tatandaan pa natin to. Now let us uh replace the symbols. Instead of CAB, pwede naman nating gamitin yung mga mismong segments. Itong AB no AB s is equal to ano yung A natin itong AE. Okay? Ae squ ano naman yung B natin? Itong ah BE BE squ na natin ngayon is AB

31:09 s equ a s + B s. So yung mga sides na iyan isu-substitute natin para makuha natin iyung missing side. Okay. Let's substitute. Aito po iyung AE natin. It's 6 cm. Okay? Andito rin sa problem. Next, BE is 8 cm. Dito rin sa word problem given. Now, we are looking for AB. Okay, segment AB. So, first simplify natin to. 6 S is 36, 8 S is 64. And then we can add 36 + 64 it will give us 100. Now paano natin malalaman yung AB? Take note, meron po tayong exponent dito na 2. So para matanggal yung exponent diyan, we need

31:55 to get the square root. Okay? So square root natin lahat nung nasa equation para matanggal natin yung square ng AB. Okay. So since ini-square na natin 'tong 100, nawala na yung uh square dito since kinuha na natin yung kukunin na natin yung square root ng 100. So what is the square root of 100? It will give us 10. Okay? Kaya av is equ to 10. Okay? So ito na po yung measurement ng ating third side or yung hypotenuse ng triangle which is the side also of our rombus. Okay. So, AB segment AB or side AB is equ to 10 cm. Okay. Now that we already got AB, ang

32:41 susunod naman na is yung ah ito yung isang hinahanap natin which is yung angle ng DAE or yung measurement ng angle DAE. Okay? Itong maliit na 'to. So let's find angle DAE. Anong property kaya ang gagamitin natin this time? Okay. So the property that we're going to use is this one. The diagonals of Arombus bisect opposite angles. So ito po yung opposite angles natin. It bisects it. Ibig sabihin it uh divides it into two equal measure. So kung 70 yung buo itong angle DA ito po yung magiging equation natin. measurement of angle DAB which is equal to 70° ay anong gagawin since diagonal AC

33:28 bisect angle DAB we can just divide it by 2 or multiply it by 1/2 okay so the measurement of DAE itong mas maliit ah imu-multiply lang natin ng 1/2 yung malaking angle or in short we just divide it by 2 okay kaya magiging 35° the measurement of angle dae is 35° using this property. Okay, so that's how we solve example number five. All right. So for our last example, example number six we have here a square glass panel will be installed on a cabinet door. Each side of the panel measures 10 cm. A metal brace will run

34:17 diagonally from one corner to the opposite corner. How long should the brace be? Okay. So ano po ang parallelogram na pinag-uusapan dito? It's a square. Okay? So mag-drawing tayo ng square. And then sabi dito, "Each side of the panel measures 10 cm." So lahat ng sides niyan measures 10 cm each. Okay? Now a metal brace will run diagonally. So diagonally ibig sabihin ito po yung diagonal ng square. So yan. And ano po yung hinahanap? How long should the brace be? So ano yung measurement or sukat nung diagonal? So in our solution, what property are we going to use? Ito po ay hindi lang iisang property ang gagamitin natin.

35:03 Actually dalawa. So yung unang property, a square has four congruent sides and four right angles. Alam natin na ang square ay lahat iyan may right angle. Ano pa po? The diagonal divides the square into two congruent right triangles. So dalawang right triangle because again we have a 90° angle. So kung meron tayong right triangle dito at alam natin onong side na ito which is 10 cm and also the same with this one it's also 10 cm kasi nga they all have equal sides. Then we can now get the measurement of this side. So anong equation natin? Gagamitin ulit natin yung Pythagorean theorem which is c s equ a² + b s. So ano ang c s natin dito?

35:52 I-label natin. Ito po yung C. Ito yung A and ito yung B. Now we can actually use D to represents the diagonal. So let's say this is diagonal ah D or let's say this is variable D. So gamit formula, papalitan lang natin yung C gawin nating D. So d squ is equ to yung a natin is 10 cm. Parehas din po sa baya we can just get their squares. So 10 s is 100. And then we can add this to magiging 200. Then we can now get the square root of 200 para makuha natin yyung value ng d. So what is the s root of 200? It will give us 10 s ro 2. Or in decimal we can have approximately 14.14.

36:42 That's why our final answer is 14.14 cm. Ito po iyung final answer natin. The diagonal is 14.14 cm. So that's how we solve example number six. All right. So finally that's all the examples that I can give for now. Uh we have here activity. If you want to master this topic, you can answer this activity. You can solve each problem. Para mas mavisualize niyo, you can show your complete solution by illustrating first the figure before you show the solution. Okay? So, i-draw niyo muna 'yung figure para mas ma-visualize niyo and then try to solve for the missing uh parts. Okay? So, ito gawin niyo po on

37:29 your own. You can check this with your teachers especially if they are using our PowerPoint presentations. Okay, so that's it for now. I hope meron ulit kayong natutunan sa ating lesson for today. Thank you for listening and I hope to see you again on our next video. Kung meron kang natutunan sa [musika] video na ito, please click the subscribe button to support this channel para mas matulungan ulit kita sa mga susunod mo pang [musika] matth lessons. Lagi mong tatandaan ang matth ay para sa lahat. At ako si teacher Van nagsasabing dito [musika] sa Mat isip lamang ang nag-iisip. God bless and [musika] see you on the next video.