lesson two angles polygons triangles and quadrilaterals all right I feel like this is a review and you maybe don't need to write this one down unless you think you do need to write it down and then you should okay but probably you know that's intersecting lines and parallel lines um I mean this is for right angle so if you have these two lines right here these are actually perpendicular I don't know if you remember that word but they make four right angles as long as they're perpendicular okay this next one it's actually this line here that is called a straight angle and so a straight angle I don't know why that line is up top it technically doesn't matter a straight angle is 180 degrees all right a straight angle is a flat line okay this other line that's drawn straight up like it could be wherever and I still have a straight angle right do you guys remember the name of these two angles what we call those that add to 180 follow me supplementary yeah that exactly we have complementary and supplementary all right sometimes like straight angle and supplementary look the same but a straight angle is just the fact that this one line on the bottom is flat so it's 180 degrees okay uh and then we've got acute angles and obtuse angles so acute angles are the ones that are less than 90 degrees all right there's a little cute they're the cute ones less than 90 degrees all right and then we have our obtuse angles which are greater than 90 degrees you guys probably remember that cool yep I see a lot of you not writing that one down okay obviously uh we have a right angle which means 90 degrees probably remember that one all right uh I don't know why we just did this one 180 in a straight line yep we got that all right and in case you forgot there are 360 degrees in a circle again I don't really know why we have these lines that's just what the book had but really you just want to know the whole circle is 360. um and then you're good to go all right what about polygons all right what is a polygon it is a closed flat geometric figure whose sides are lying segments uh these guys right here not polygons all right why are these not polygons these like cross in the middle I suppose you could say these are two separate polygons here but they can't do that can't have lines across you can't have these like not be connected all right and this is a problem because it's curvy all right so that is not a polygon so here are like some polygons all right I would write this part down at least for like what the name of each one is in case you forgot all right so everyone probably knows this one what is the name of this polygon everyone great job triangle all right what is the name of this one the most generic form Ula yes quadrilateral just any four-sided figure I know that looks like a square it probably is a square right uh but just the generic four-sided uh figure is a quadrilateral all right okay uh five sides anybody know five everybody who knows it good job pentagon okay how about six sides anybody knows six hexagon okay anybody know seven uh accepting on I don't think is right although I feel like we've used that for something else but it is not a septagon does anyone remember uh it is a heptagon tricky all right so seven sides is a heptagon all right how about eight octagon okay and I can't draw them apparently I just stopped drawing him you have to just picture that in your head okay nine sides anybody know nine sides yeah nonagon nice job anybody know ten sides yep good job decagon okay anybody know eleven sides it is an undecagon and anybody know 12 saw 12 sides yeah close it's a doe decagon and N sides is an end gone yeah so it's just a 13 gun or a 14 gun or a 15 gun after that all right until it just becomes a circle um did you guys still need to write sorry some of you looked at me like you were not done all right we have con cave and Khan Vex which one of these is Khan cave the left or the right everybody yeah so this guy right here is concave okay it like indents all right so if you can draw a line like this and it goes like inside that is concave all right and then convex is this one right here so concave makes like a cave all right convex they're all pushed out nobody's indented okay uh regular polygon has to have both of these things true all right so raise your hand if you know what equilateral means um what's your name again Kira what is it exactly all sides and I'm gonna use this little symbol that means congruent in Geometry which is equal okay they're all equal so if I had an equilateral triangle that was not drawn very well but all of those sides are equal okay equal angular raise your hand if you know what equilangular is Eli exactly all oops all's all angles are congruent all right so if I had an equal angular triangle this angle would have to be 60 this one would have to be 60 and this would have to be 60 because the odd 180 they're all the same all right now if both of these are true we have a regular polygon so if you hear or see the word regular that means that all the sides are equal and all the angles are equal all right so here I have a regular hexagon where I have equal sides and I also have equal angles it is regular all right let's talk about the different kinds of triangles and let's see raise your hand if you can tell me what type of triangle this is right okay good this is a right triangle excellent what else what other kinds of triangles do we have okay we have obtuse okay I like it this would be obtuse because this angle is greater than 90 if one of the angles is greater than 90 we have obtuse we have another kind of triangle let me remember another kind yeah we have a cute uh I'm not sure if this one is a cute they all have to be less than uh 90 but like so this one right here where they were all 60 would be acute right anybody remember when all the sides are different lengths what it's called um Kiera yes scalene all right and this would be scalene right here because those are definitely all like different lengths yes yeah we also have isosceles oh that's coming down here all right isosceles which one is isosceles of those three you guys this one right here okay I saw Solis that means that two sides are the same length if two sides are the same length we also know and this is kind of important that the base angles are the same okay that's something that's important to know all right so this one right here we just learned the vocab word for what's that called equilateral okay that's equilateral and then this one is scalene all right oops all right a little review about triangles uh raise your hand if you remember what all the angles of a triangle add up to Ryan yes 180. so I call this Triangle Sum in Algebra 2 we make you write down tf's for Triangle Sum which basically just means all angles add to 180 okay for any triangle they add to 180. so we need to find X we'll we'll write a little equation here okay you can write your uh your work like this or you can do 180 minus 30 minus 130. however you want to do it all right if you want to write an equation or if you just want to show that you subtracted from 180 that is fine with me um so this would be 160 all right subtract 160 from both sides so X is equal to 20 degrees and in in algebra two you will write TS Triangle Sum like that's how you were allowed to do that you don't have to do that for this class class okay all right so there you go give you guys a minute it'll do so riding I go kind of fast on some of the review stuff all right find X and Y what kind of triangle is this everyone isosceles all right we have two sides the same so this guy right here is telling us this is equal to this so someone raise your hand and tell me which angles are equal so as soon as you see isosceles you better check for equal angles is it Marshall yeah yeah okay what's the what's equal exactly right here I know that this is equal to this so there's a little note here it says in any triangle the opposite sides of equal lengths have equal angle measures all right so opposite of this side is this angle opposite of this side is this angle so since they're equal these are the base angles if it was turned you might want to check for opposite those sides it's not always the base angles you know what I'm saying all right so check if it's like looks like this that was terrible but pretend like I drew a good triangle there and those are equal all right then obviously it's these two angles that are going to be congruent okay all right so anyways X is 50 degrees and in Algebra 2 you actually write i t for isosceles triangle but you don't have to do that in this class but that's how we know all right the base angles are equal because it's an isosceles triangle but you don't have to do that here okay we still have to find y so now I know that y plus 50 plus 50 is equal to 180 because of Triangle Sum it's just ingrained in me to do that now but again you don't have to do that okay so the whole thing has to add to 180 I know the two are 50 so that's 100 I'm going to subtract 100 from both sides so I know that top angle is 80 degrees any questions okay we'll try one more I guess all right what kind of triangle is this yes and it is isosceles how do we know it's isosceles since it's not actually marked uh live [Music] yes so notice this these are both eight Eight's equal to eight okay so now someone told me which two angles are equal because you got to know like based on someone I haven't called on yet is it Knox it is Y and X exactly okay so this is opposite and then opposite the side so those two angles have to be equal all right so how would we solve Nolan yeah exactly all right so each of these have to be 35 degrees all right so subtract one from 180 and there's 70 degrees left over and then they have to be equal so divide by two any questions all right very good unfortunately we have more quadrilaterals label the following quadrilaterals all right these are just all the names for four-sided figures so like raise your hand if you think you know what that first one is is anyone who has not participated that would like to maybe uh suggest something is it Claire okay oh you are close all right Cara go ahead yes we'll go with parallelograms so a rock parallelogram all right a rhombus has to have all sides equal all right so it does have parallel sides but all sides are equal so parallelogram just has parallel sides okay uh how about the next one Sonya trapezoid great okay how about the next one Kade yep and now what is this one Claire yes now we have a rhombus all right and this last one everyone good job all right so those are just some things we'll go over kind of all of these um because remember a square can be a rhombus but like a rhombus can't be a square not necessarily a square those are that gets fun yeah we'll not worry about that for now that's just the basics all right you guys that's it