 So we went through all the way up to Somewhere here it should say ah stop there So turn to what was called question number nine for some strange reason And I want to show that these two triangles are congruent How I have no idea I'm gonna let the givens guide me and I'm looking for side side side side angle side And angle side angle all that good stuff So it says well Adam what do you think I'm gonna write here? Adam I Think I'm gonna go x y equals. I'm not gonna go z y American boy You know what I'm gonna go with a proud maple leaf etched on my heart I'm gonna say zed why my friend zed Because that's how I roll That reason so since there's two blanks. I would go half mark half mark. Oh Did I just write something down Marcus? I better mark it on my diagram x y Boom boom is the same size as zed why What do I now know now? There's more givens, but also I've just realized the great big triangle Boston is isosceles I'll bet you I'm not looking, but I'll bet you my next line probably wants me to mention something about that Does it oh what ah? This angle is The same size as that angle Because if a triangle is isosceles Alex to side boy I'm watching that even worse of it make it look like it has two hash marks two sides the same means two angles the same two angles The same means two sides the same so I can call this angle Y X X mr. Do Y X W is angle Y ZW and Right now in terms of congruency rules Emily. I'm thinking either side angle side Maybe or angle side angle maybe people come in Well Jordan there's two more lines left and I know my last line by the way is going to be Triangle X W Y Equals congruent to triangle ZW Y. I know that's going to be the case I don't know what I'm gonna put here side angle side angle side angle or angle side or side side Any suggestions? Oh? Have I used all my givens yet? I'll bet you you know what Sierra. That's gotta be this line here last given Because I haven't used all the information they gave me and in a court of law Why wouldn't I use the evidence that I had people's exhibit one people's exhibit two so angle X Y W is the same size as angle Z Y W angle X Y W that's this one here is the same size as Z Y W. That's that one there given and Hey, which congruency rule have I forced that into here angle side angle So give yourself four marks one mark for each line if there's two blanks online half mark for each blank Shania are proofs tough. Yes. Ah, but are they also tough to get a zero on? I'm hoping you can all get the givens if nothing else Right and the show So It's a you know Tough to get perfect tough to get blank. Ooh a five marker five lines Shay, what am I gonna write in line one? You don't say I mean don't say yeah AD equals BC Am I gonna move on to the next line? No, I'm gonna write this on my diagram because you try and keep track of all of these in Your head is ridiculously tough AD This is the same length as that and we show length with hash marks. How do we show parallel arrows? Oh And given that Matt, what is my next line gonna be? Okay, so I'm gonna go AD is Also parallel to BC parallel is gonna be one arrow one arrow or two arrows two arrows or three arrows three arrows I've made that up whenever no. Oh, come on. I see dead people. I see that I see Except for Adam, I see a Z I'm willing to bet that my next line because I'm saying why would we have to enter this into evidence Adam? The only thing I can think is I've got a set. I'll bet you my next line is gonna be This angle here is the same size as this angle here Angle ADB is angle CBD and Just like last day Matt as long as the D is in the middle in the first one and the B is in the middle on the second one I don't care what you have to see me Why do I know those two angles are the same? What was the Z rule? Alternate interior and I now have angle. Oh, no, wait a minute. I have side angle or Angle side So Emily, I'm either going to go side angle side or angle side angle Hmm. Oh DB equals DB. Oh What did we call this one remember what we actually just wrote? Yeah, same side common side if you want if you're British and I told you last day I tend to show the same side with a big slanty S on the first same side and Now Courtney, I've got a congruency Do you see it? Which one which rule angle sides angle side angle side or side side side Did you say side angle side? Did you not? Could you do both of those with a bit more volume so I can think you're right? Have some pride hold your head up me. I'm smart side angle side and it's gonna be the last line triangle ABD is congruent to triangle CDB Five marks Last one To do it. I found these last three easier than the other ones. I think they might have been but I think also you're getting better Boston read the first line to me. I'm gonna mark that because it's given ED boom boom equals EF boom boom. Okay, and Then it says Boston angle D equals well This angle right here How big does it? What's the other angle? It has to be the same size as Sorry, what goes here? Why you're saying they're the same because they're the same that's called circular reasoning Why are they the same? Here's your hint Look at the previous line that we entered into it No, no, no, no, no, no, no, it's not given give is it written here that those two angles are the same What I'm saying is though, why did they need to tell me this? What about this? Let's me make this assumption people Yeah, that's why they had to tell me that otherwise I could not assume line two without them telling me line one was correct That makes sense Good By the way, I repped after school yesterday. I repped two games the day before I repped a game the day before My voice is on its last legs. I'm not on a grumpy mood. All I have right now is loud angry voice So if it sounded like I was getting on your case, I'm actually enjoying teaching you if I go higher and more polite I got nothing. Sorry feels weird Almost sound like mr. Goulet or maybe not quite that bad Marcus, what am I gonna write on my next line? I guess my next given because that's a given Dg equals gf. I'm gonna mark that Dg E123 Equals gf new one two three. Oh Which congruence you rule have I just forced that into here Sierra? See it darn right That's my last line and the statement's gonna be triangle D E g is congruent to triangle F D give yourself a score out of three give yourself a total score out of count them 12 Put your name on it Pass them down to the end of the row and I'll walk down the middle and collect them and the person in the middle We'll put them in a nice neat pop get your calculators out if you haven't already We paused right there last day on our wonderful review of Pythagoras But now we're gonna start to try and get into tougher questions this year as well We're not just gonna say here's a triangle fill in the blanks a little bit But we're gonna start to give you what are called compound diagrams diagrams of more than one triangle of overlapping triangles multiple steps The nerdy cool stuff Let's look at finding a missing leg. So it says find the missing side Example three is this a right angle triangle Sierra So I can use Pythagoras So I'm gonna write down a squared plus b squared Equals c squared what always has to go where the c is the hypotenuse What's the hypotenuse here? I'm gonna have to put the 73 squared right here a and b it doesn't matter I'll put the x squared first because I kind of like to see the x in front and then the 55 squared here now what I need to get the x squared by itself How okay, and again if you can do this in your head showing No work if you just go straight to going x squared equals 73 squared minus 55 squared I'm good with that now we get at our calculator. What does x squared work out to what is 73 squared minus 55 squared? I have no idea 73 squared minus 55 squared equals 2304 Jordan how do I get out of a squared? So when I square root this what do I get Jordan? I think you said the answer didn't you thought I heard it no evenly Wow my friend who made this up clearly Knows more triangles than I do that work out evenly. I never I don't mind decimals I Guess centimeters Devon how much of this do you have to do in your homework? In our notes, let's show all our work so that when we're studying we know what the heck we did But Sydney I'll be honest if you can go straight to your calculator and If you look at this and you know it's going to be this squared minus this squared and you go straight to your calculator and Then you press your square root button of your answer on your calculator and you straight write an answer I will take your what you didn't cheat because I think that's how good you should be so in the homework The answer is right the back of this if you just write an answer Simon I'll assume you didn't bother just flipping to the back writing the answer that I didn't do it I'll see me get it on your calculator, and I'm good with that. Would I do that on a test? You always want to show extra work on a test in case you make them a straight I don't get the wrong button on your calculator. I don't notice it I can still get part marks and mr. Do it saw my work that usually on a test I only give a half mark for the answer. I give everything else for the work example for a 5.3 meter ladder is leaned against the wall so that the foot of the ladder is 1.2 meters away from the base of the wall Huh? Devon, what does that stand for? Draw a little picture ladder Says lean so there's my leaning ladder wall Floor where's this 5.3 gonna go and also Alex 90 degrees? Where's this? Wow Where's this 5.3 have to go so here here or here? Right there Where's the 1.2 gonna go Jordan? Now we can do a process of elimination if you're not sure Jordan. What are they asking me to find? I'm pretty sure that's where I'm gonna put that's how high yes Which means by default? I'm pretty sure that's the base 1.2 meters away from the base of the wall All right, let's take a bit of a shortcut. We have Pythagoras written right here. Yes, so Marcus Can you just read to me what squared plus what squared equals what squared? Don't read the ABC? I'll give you a hint x squared plus Yeah Yeah, how I have it squared equals Yeah, if you go straight to that now, I'm good How do I get the x squared by itself Marcus? So x squared is gonna be 5.3 squared minus 1.2 squared We'll write this in our notes again in your homework if you want to Boston go straight to your calculator as long as you're getting them Right, I will trust you to do that. I will also trust it. You're getting them wrong. You'll show more work Yes, Erin make sense Erin what do you get what is x squared? What is 5.3 squared minus 1.2 squared louder to six point six five Okay, how do I get rid of a squared Aaron? Oh Square root that for me, please What do you get five point one six even or five point one six blah blah blah junk Okay, what's after this you drowned off properly what's after the six a two okay five point one six meters Last and this is probably the new part Multi-step questions a ramp is placed on two cement blocks that are one point two meters apart If the blocks are two point three meters and four point one meters high respectively in that order Find the length of the ramp say what I think what we're saying is this small cement block big cement block Ramp, believe me. You don't want to try me drawing these by hand. I suck. I'll cheat and use the software What else have they told me? Now we look for numbers What's one point two how far from here to here more importantly How far from here to here because I'm trying to get a triangle 1.2 meters Joe, what's the next number they gave me? Okay, where's it 2.3? Oh? Right here 2.3 meters from here to here Is that right? What about that next number Joe from here to here? What do they want me to find Adam? Where's that oh ah That yes, okay They want me to find C squared. There's a squared up. Ooh. Do I know B squared or B? Jordan's nodding his head. I don't think I do yet, but are you rubbing your eye? I thought you were nodding your head well Jordan How long how long How long 2.3? What's left? How you getting that? How you getting that ah? So they don't need to tell me this I can figure it out 4.1 minus 2.3. How long is This side right here is it 1.8. What's my equation going to be what squared plus what squared equals what squared? Shania equals x squared Is the x squared by itself already? Oh, that's nice So let's go to our calculator square root of that and I get x equals 2.16 for me Could I could have gone to two pot after the sixes I get a three I Could have gone to 2.2 because they went to one decimal place when in doubt I usually go to two decimal places as kind of my dollars and cents rule of thumb there whatever last one example six in the diagram below ooh We understand this now because you've done geometry ad equals 26 millimeters. Let's add that Bd equals 31.5 and ac equals 10. What do they want me to find? AB this picture actually has three triangles in it The great big one The right hand one and the left hand one and Jordan I'm kind of eyeballing this but this great big one here I don't think I can use Pythagoras because this angle here. I think looks bigger than 90 to me So I'm gonna have to use either the right hand one or the left hand one or both now I'd like to start here, but to do Pythagoras. I need to know two sides. I only know one So even though this says find x I think I'm gonna spend more time Courtney trying to find this side How can I find how big this is? Jordan so you're saying do Pythagoras in the right triangle and that'll tell me Hey, how about I put the letter y since I used x up already There it is then I go 31.5 minus y gives me that Hey, what letter would be smart to put here if I've already used up x and y hang on Adam what letter would be smart to put here if I already used x and y what would be a Z? Absolutely, what it's doing. Mr. Duke. I am Canadian. Sorry all right We've got our procedure then you hear what Jordan said find y first and Then go 31.5 minus y gets you zed and then Pythagoras in the left-hand triangle to find x good Try it on your own. I'll do it up here. Let's see if we end up in the same spot. Yeah No, I'm wrong. Did you get 24 for y? So double-check your you got to be didn't get this Here's where I found y here's where I found zed. Here's where I found x. See where you ziggid 12.5. Yeah, or no. Yeah worked out evenly sort of I'm amazed See it if not object if you didn't get this call me over in a second. Yeah Okay, I'll come look in a second. Let me get everybody going first Goal is no homework for the weekend. So I wanted to give you lots of time to work on this your homework is number one number two three a 3d 3e 3f Four five is nasty if you get it. I'm impressed. Okay, so I signed number one all two all three a and d E and f four and five you got the holy smokes 40 30 40 minutes to finish it off. Let me take questions here