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.
