# Question Video: Completing a Sentence About Special Cases of Parallelograms Mathematics

Each of the two diagonals of the square makes an angle with a measure of ＿ with the adjacent side.

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### Video Transcript

Each of the two diagonals of the square makes an angle with a measure of what with the adjacent side.

Let’s consider what we know about a square and its properties. A square is a type of parallelogram with four congruent sides and four congruent angles. Notice these angles are all 90 degrees. Because squares are a type of parallelogram, they inherit all the properties of parallelograms plus all the properties of rectangles and rhombuses.

Now because we are considering the diagonals of the square, let’s recall the important properties about the diagonals in a square. Firstly, in any and all parallelograms, we know that the diagonals bisect each other. Secondly, because a square is a type of rectangle, we know that the diagonals will be congruent. Thirdly, coming from the properties of a rhombus, we know that the diagonals bisect opposite pairs of angles.

In this problem, we need to consider the measure of the angle that the diagonals make with adjacent sides. For example, what is the measure of this angle marked on the diagram? Well, we know that the two sides of the square make a 90-degree angle. And we also know that the diagonals bisect opposite pairs of angles. This angle of 90 degrees is therefore bisected, or divided by two. And we know that that will be equal to 45 degrees. Because the sides are congruent, this will be true of every angle created with a diagonal and an adjacent side. We can therefore give the complete statement. Each of the two diagonals of the square makes an angle with a measure of 45 degrees with the adjacent side.