SM2 9.2-1 Angle and Side Properties of Parallelograms

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[00:00:00]Hello and welcome. So we'll be talking about  parallelograms today. So we're given that ABCD is a parallelogram. Find the measure of each  angle. Um, on the other one we're told that we have the segment CD is 42 and we need to find  the other segment AB. Okay. So let's just go left to right. First let's worry about this one  on the left. So when it comes to parallelograms we know two things about its angles. We know the  angles that are opposite, right? Direct opposites are congruent. So that means that whatever this  angle is, which is 148, is this angle down here.

[00:00:36]This is also 148. So that means angle C is 148  degrees, okay? Well I guess you don't need a degree symbol since it's right there, okay? Most  of the time you won't have to write the degree symbol. I just write it out there by habit, okay.  And then the other thing we know about angles for parallelograms is that we know that adjacent  angles, so angles that are side by side. So for example if you look at this angle right,  you'll kind of notice that these two angles, this one and this one, they are adjacent.  They're next to each other, right? They're not across from each other, they are next  to each other. That means they're adjacent, okay? And in parallelograms adjacent  angles are what we call supplementary, which means that they add up to 180 degrees.  So what that means is that your angle A and your angle B they must add up to 180. That  is what it means to be adjacent angles, they add up to 180. So you say okay well angle  A we already know that's 148. Angle B we don't know but we do know it adds up to 180. Solve it  like an equation, right? Subtract the 148 both sides and then you just have 180. Right 180 minus 148  and then from there you'd have angle B equals 32 degrees. Bam. And as soon as you know that  you could use another adjacent supplementary angle to get D, but once you know that this  is 32 isn't that directly across from angle D?

[00:02:11]And we know the angles that are directly  across or in other words opposite of each other are congruent. Bam. Okay, now you know  all four of your angles. You're good to go.

[00:02:22]Okay, when it comes to sides of a parallelogram,  um, the only thing you can say about the sides, there's no relation that relates AB and  AD together, but we do know that sides that are directly opposite to each other. So  we're given CD, opposite of that would be AB, and in a parallelogram whatever this is, is  the same value of whatever that is. They will always be congruent or the same. So likewise if we  knew AD or BC we would be able to find the other side because those are also congruent to each other. So that means that if CD is 42, AB is 42.

[00:03:04]Okay. And that is all of your properties  for parallelograms. Thanks for watching.