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7.2 Notes AP

Added Jan 29, 2016 •

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okay guys one of the main things about doing these videos is remember that you can pause and Rewind and re-watch as many times as you need your note and then if you have questions for me you can ask when you get to class and start doing your homework also now if you look this is section 7 what chance parallelograms the rest of this chapters going to focus on quadrilaterals remember a quadrilateral is just a polygon with four sides so any polygon with four sides is called a quadrilateral this lesson is going to Folk just on parallelograms and you should have the formal definition in your notes but just remember that it is a quadrilateral with two pair  a parallel side so if you look down here baby CD you're going to be parallel to each other  and BD and AC are going to be parallel to each other so basically the what sides are going to be parallel properties and that's where we're going to get out of these theorems that are all listed below okay the first to have to deal with the opposite sides in the opposite angles and look at 7.3 parallelogram opposite side theorem if a quadrilateral is a parallelogram then it's opposite sides are congruent so opposite sides are congruent now if you look right here that means these two are congruent and these two are congruent QP NRS so if we Mark that up here that would mean the top one and the bottom one are congruent and two sides are congruent now or next them is 7.4 parallelogram opposite angle theorem and what it says is if a quad how does a parallelogram then it's opposite angles are congruent so if you look at this picture r&p or congruent q&s so the opposite are congruent to each other now they're not all the same you have two pair of that are the same this pair of the same in this pair of the same so if we go up here in me Mark that all of what will be will be congruent to all of angle C and all of angle D will be congruent to all of angle a right now we have opposite sides are parallel and congruent and opposite angles are equal okay the next thermos 7.5 parallel parallelogram consecutive angle theorem now consecutive angles where have you seen consecutive angles before with parallel lines so if I draw that over here real quick remember consecutive are on the same side both interior they were consecutive interior and these are supplementary versus are alternate interior angles were equal now think about this being a parallelogram these two right here or between the parallel lines so they correlate with these two they are supplementary just like when we had parallel line so if a quadrilateral is a parallelogram then it's consecutive angles are supplementary but how many pair do we have soci I hear then x + y is 180 well here's x + y here's x + y here's x + y and here's x + y so any set of consecutive angles is 180 so people assess equals when i r + S equals when i t r + Q as when I Q Plus P so let's go up here and lay that on our little diagram so if we did D&D together they're going to equal 190 degrees and if we do a and C together they're going to equal 100 any degrees now likewise if we do A and B together they equal 180 degrees and if we do c and d what is there going to be a hundred degrees so every set of consecutive angles equal 180 degrees the parallelogram diagonals theorem now remember diagonal in a parallelogram a parallelogram diagonals of a parallelogram diagonals theorem says if a quadrilateral is a parallelogram then it's diagonals bisect each other okay so if you will look RP by 6 qso qsr is cut in half they're both 1 Mart and Key West by 6 so it's cut in half so see they're both too much so if we go up here and we draw that on our diagram that we have here and we already have one marks and to Mark so we're going to have to do something different so this one will be three more M3 Mart so ad is cutting half a day and then CBS cut in half so we'll give those four marks okay so here's what we've got look at this parallelogram and everything you know about opposite sides are parallel opposite sides are equal opposite angles are equal consecutive angles equal 180 and then diagonals bisect each other is diagonals cut it into 4 triangles and you can even get in further on this and really start looking at stuff cuz you got parallel lines you got triangle you got all kinds of stuff that we've already looked at all together in one  so if we look at this  look at these two triangles look for Mark 3 Mark to mark for Mark 3 Mark to Mark these two triangles are congruent by side side side so we could actually say that triangle a b c  aec now a goes with the two marks of Dev are congruent  K LifeWise look at these two there's a one Mark at 3 41 Marcus 3 and 1/4 of these two are congruent so we could actually say triangle CED on the bottom is congruent triangle Bea on the top then you got all kinds of angles that are congruent to each other you also have parallel line put the transversal so you have alternate Interiors or equal alternate interior equal then these you got supplementary here here hear you got vertical angles here you got all kinds of stuff just within this one parallelogram so besides these four properties there's other thing that you know have to be true because of all the markings from these properties okay that is everything you need to know about parallelograms and you just have to apply those properties to problems solo look at these problem zoom in look at number one what do we know in what can we said he will all the sides are marked so we know opposite sides are equal those two are equal please try to do this one and this one first I got an X and Y so that may not be the smartest thing let's look at this pair like an accident they're equal synonym equal soft 4 x o x + 18 equals 3x minus 2 I would subtract my X on both sides and then I would add my two to both sides so those cancel so now I have 20 close to x / 2 x equals 10 so there's X now we need to find why so we know this pair is equal so we can say that for x equals y but we already know what x equals so we can put the 10 in right here so why equals 40 so X estimate NY has to be 40 in that picture because it's a parallelogram look at number two very similar we have this side congruent to that side and then they give us a pair of opposite angles these have to be equal each other so we know this angle is equal to that angle so start out with the Angles and if you do 4X minus 37 equals 49 you would add 37 to both sides those canceled you get for x equals 86 divided by 4 and you get x equals 21.5 so now I know X then I can sit up two sides equal and I know this ex is going to go right here now go ahead and put that 21.5 + 4 * 21.5 - 3 if you do that you were going to get 83  so 83 is equal to why / 5 now the easiest thing to do is put that over one and just cross multiply so you get y equals 400 15 game so X is 20 .5 and Y is 415 all right let's look at number 3 number 3 they give us diagonal what we know this diagonal and we know this diagonals cut in half so that means that these two are equal and these two are equal these are wise these are exes doesn't matter which one you saw first Fair because we have two wives or we have two axes so let's do the X's first 2x + 10 equals 4x - 2 that's this and this one now just saw I would subtract the two x from both sides and then add the two to both sides so those cancel you get 12 equals 2x  divided by 2 + x equals 6 play and then if we do the wise this one is equal to this one so 5y - 16 equals 3 watt now because why is already by itself on the three wide side I would go ahead and minus 5y to both sides when you get -16 equals -2 wide add by -2 and you get y equals 8 so x equals 6 and wife was 8 for that problem okay for this one it says in 4th or 11 find the indicated measures in a parallelogram mnop explain your reasoning so you can find that in you can tell the serums if you want to but look at this we have diagonals what do we know about him they're cutting half so this one is play run to this one in this one's congruent to that one well if that one's 14 this is 14 and this one has to be 20.7 what do you know about opposites lights will if this one's 24 this one has to be 24 and if this one's 26 this side has to be 26 then we also know the Opposites are parallel now the other thing we know our angles so let's look at the angles  is this English yay that's pointing to the whole thing we know this whole angle is 68 so I know that one's going to be 68 degrees I know anything about angle M & O well remember that consecutive angles add up to 180 so p + m is when I V so is 180 O+ in is 180 in + m is 180 so if we do $180 - 68 we get 112 So this whole thing go right here is 112 and this whole angle I guess I should put to March is 112 now they give us that this part is 59 so how can we find this part well subtract 112 - 50 that'll tell you what this angle is cuz they have to add up to 12 so if you do that you are going to get 53 degrees now the other thing is you do have parallel lines here so alternate Interiors are equal so this is this is 59 5353 just like that so here I have 53 I have 59 now why can we not do that on this one cuz we don't know the part and they're not cut in half we just know they add up to a 68 here in 68 here but we don't know one of them to find the other part so that we have to leave the whole angle is 68  and by doing all of that we have probably answered every single question that is over here so just fill in for what is p o p o is this one well we said that was 24  number five is uo-2 Q we said that was 14 the next one is in Ono side we said was 26 the next one is PQ so PQ is right here we said that was 20 points who am I going to Ingles came so let's look at our angles this one is soap p.m. in this whole one so we said that was 112 degrees  the next is NOP NOP this whole angle so the whole thing is 112  the next one is op OPM so it's this whole angle and we said that whole thing was 68 in the number 11 is nmo in MO now that one is just this half and we said because there alternate interior the same as this one so it's 59 degrees  and then the last one that was the last one so we're done now that's telegram That's the basis you just need to know the properties and everything that goes with it if you need any help just

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7.2 Notes AP

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