Hi, and also welcome to this video clip on diagonals! today we’re walk to discover the diagonals of parallelograms, rectangles, rhombi, and squares, and also see just how these forms relate come each various other overall. Let’s get started!
All of the forms that we room going to look at today are quadrilaterals, definition they room all four-sided polygons. A polygon is a shape with lot of sides.
You are watching: Do the diagonals of a rectangle bisect each other
Types the Quadrilaterals
Properties of a Parallelogram
A parallelogram is a quadrilateral that has two set of parallel sides. The blue arrows denote which sides are parallel to every other. The opposite sides of a parallelogram, significant by green tick marks, are congruent, which way they have the exact same measure.
Properties that a Rectangle
A rectangle is a shape we all know well because it appears in the real human being so often. Yet one point we don’t usually think about is that rectangles are simply a special kind of parallelogram. That means that opposing sides are both parallel and congruent, just like our an initial parallelogram. What makes a rectangle a special parallelogram is that its interior angles room the same. In fact, they room all right angles, which method they measure up 90 degrees.
Properties the a Rhombus
another special parallel is a rhombus. It has all the properties of the parallel but every one of the sides of a rhombus room congruent. Note that the tick marks space all the same, which tells united state that all the sides room the very same length.
Properties the a Square
our last one-of-a-kind parallelogram is a rectangle and a rhombus at the same time, for this reason it has the appropriate angles of the rectangle and also the congruent political parties of the rhombus. It’s one more shape we all understand well: the square!
As you have the right to see, the opposite sides are parallel, all the angle are appropriate angles, and all the sides are congruent.
So stop recap our quadrilaterals prior to we start exploring their diagonals:
Here, we’ve arranged our quadrilaterals right into a sort of “tree”, starting with the square as the trunk. Every square is a rhombus and also every rhombus is a parallelogram. Every square is additionally a rectangle and every rectangle is a parallelogram. That’s just how it works going up the tree. But it doesn’t occupational going down. No every parallel is a rectangle and also not every rhombus is a square.
Okay, now let’s explore the diagonals of these four quadrilaterals. A diagonal line is a heat segment connecting the opposite vertices, or corners, of a quadrilateral.
Diagonals that a Parallelogram
here’s our regular, non-special parallelogram through the diagonals shown:
As you deserve to see, the diagonals that a parallelogram bisect every other. In other words, they cut each other in half. We could include some numbers to show this better…
or we could use tick marks to show that the diagonals have actually been bisected:
Since the 3 special quadrilateral we’re talking around are every parallelograms, they will certainly all have bisecting diagonals.
Diagonals of a Rectangle
currently let’s look in ~ the rectangle. This is a rectangle v its diagonals:
The diagonals the a rectangle room congruent, and, again, since a rectangle is a parallelogram, the diagonals bisect every other, making each half the exact same length:
Each diagonal of a rectangle also divides the rectangle right into two congruent ideal triangles:
This method that, if we wanted to, we might calculate the size of the diagonal utilizing the Pythagorean Theorem.
Diagonals the a Rhombus
currently that we’ve acquired rectangles figured out, let’s watch what wake up with one more special parallelogram, the rhombus:
Once again, because every rhombus is a parallelogram the diagonals bisect each other. The diagonals room NOT the same size though, so what’s special about this one? take it a look at the angles at i beg your pardon the diagonals intersect. These angle look like they might all it is in the same, and since over there are 4 angles over there it should mean…
That each angle is 90 degrees! This method that the diagonals the a rhombus are perpendicular to each various other in enhancement to bisecting every other.
Diagonals that a Square
Okay, only one square left, the square. Remember, the square is a parallelogram, a rectangle, and a rhombus, so the should have actually all the nature of those shapes:The diagonals will certainly bisect every other.The diagonals will certainly be the exact same length.The diagonals will be perpendicular to every other.
Let’s check out if we’re right:
We to be right! If us look closely, we can also see that the 2 diagonals cut the square into 4 congruent isosceles right triangles.
currently that we’ve looked at our four parallelograms and also their diagonals, let’s end up with a testimonial to see what all you have the right to remember.
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Which of the following statements is false?Every rectangle is a parallelogram.Every rhombus is a square.Every square is a rectangle.The diagonals of a parallel bisect each other.The diagonals of a rhombus crossing at best angles.A diagonal line of a rectangle divides it right into two congruent ideal triangles.The diagonals the a rectangle are the very same length.A square whose diagonals bisect each other, intersect at right angles, and also are congruent need to be a square.