### Video Transcript

Consider the figure, then complete the following using less than, equals, or greater than. ππ what ππ.

So, letβs have a look at the shape and see what we can tell about it. To start with, itβs a quadrilateral, a four-sided shape. And within our quadrilateral, there are two triangles. This small line on line ππ and line ππ means that these two lines are equal in length. And weβre given two angles that are both equal to 39 degrees. So, we know that the measure of angle πππ is equal to the measure of πππ. And thereβs one other thing we can say about this shape; the line ππ appears in both triangles, so that means that itβs common to both triangles.

So, if we were to consider the attributes of both these triangles, triangle πππ and triangle πππ, then we can say that they each have a side length that itβs the same length. Line ππ is equal to line ππ. They also both have an angle which we know is the same size; the measure of πππ is equal to the measure of πππ. And finally, we know that they have yet another side thatβs the same length; the line ππ appears in both triangles.

Since the angle that weβre given is the included angle between the two sides, that means itβs in between them, this means that we can use the SAS or side-angle-side congruence rule. This means that we can say that triangle πππ and triangle πππ are congruent using the side-angle-side rule. If two triangles are congruent, that means they are exactly the same shape and size. So, corresponding angles and sides will be the same in each triangle. So, for our angles, that means the measure of angle πππ will be equal to the measure of πππ. And the measure of angle πππ will be equal to the measure of πππ.

And for our lines, we were already given that the line ππ is equal to the line ππ. And we know that the line ππ in both triangles is equal because itβs a common side. And finally, since weβve established that our triangles are congruent, this means that our third sides, ππ and ππ, must also be the same length. So, we can write ππ equals ππ, which means that the missing symbol in our question is equals.