### Video Transcript

Which is the correct relationship between π΄πΆ and π΄π΅, a) where π΄πΆ is less than π΄π΅, b) where π΄πΆ is greater than π΄π΅, or c) where π΄πΆ is equal to π΄π΅?

To help us solve this problem, weβre actually gonna use something called the angle-side relationship theorem. And the angle-side relationship theorem says that in a triangle, the side opposite the larger angle is the longer side. So therefore, the angles that we want to find are π΄π΅πΆ, because this is opposite π΄πΆ, and the angle π΄πΆπ΅, because this is opposite side π΄π΅.

Okay, so letβs go on and find some angles. So first of all, weβre gonna start with finding the angle π΄πΆπ΅. Well angle π΄πΆπ΅ is gonna be equal to 61 degrees. However, we do need to give reasoning for this. Well, if we have a look at the diagram, we can see that we have two parallel sides. And these are shown by the arrows.

So therefore, as they are parallel lines, we can say that angle π΄πΆπ΅ is equal to 61 degrees because alternate angles are equal. And Iβve actually highlighted the alternate angle with a little red mark so we can see that 61 degrees and the π΄πΆπ΅ are going to be the same. Sometimes theyβre called π angles because of the shape they make.

Okay, so now we found angle π΄πΆπ΅. Letβs move on and find angle π΄π΅πΆ. Well again, when weβre trying to find angle π΄π΅πΆ, what we want to do is we actually want to look at the fact that itβs a pair of parallel lines. And due to this, we can say that angle π΄π΅πΆ is equal to 67 degrees. And we can say this because angle π΄π΅πΆ and angle π·π΄πΈ are corresponding angles.

And therefore, because theyβre corresponding, theyβre going to be equal. And Iβve just shown a little sketch, what angles would be considered corresponding. And as you can see, thatβs like our angle π΄π΅πΆ and angle π·π΄πΈ. Okay, great! So weβve now found out the two angles, 61 degrees and 67 degrees. So then we just need to remind ourselves that angle π΄πΆπ΅ is opposite π΄π΅ and angle π΄π΅πΆ is opposite π΄πΆ.

And we know that angle π΄π΅πΆ is greater than π΄πΆπ΅. And we know this because 67 degrees is greater than 61 degrees. So therefore, if we look at the angle-side relationship theorem, where it says that in a triangle the side opposite the larger angle is the longer side, we can say that π΄πΆ is greater than π΄π΅. So therefore, b is the correct relationship between π΄πΆ and π΄π΅ because, as we said, itβs where π΄πΆ is greater than π΄π΅. And this is because angle π΄π΅πΆ, which is opposite π΄πΆ, is greater than angle π΄πΆπ΅, which is opposite π΄π΅.