What space quadrilaterals? In this video, we check out that question and also more. Reap — and then be sure to watch our various other Geometry videos!

You are watching: A parallelogram with 4 congruent sides

Image by Volha Stasevich

Some human being think about this as a diamond shape specifically if we orient the this way. We orient it through the 4 points pointing horizontally and also vertically. Diamond is simply kind of a casual or colloquial means to refer to a rhombus. For this reason rhombuses space parallelograms, so they automatically have the large four properties. Every rhombus has the huge four properties true that we just talked about.

### Two one-of-a-kind Rhombus Properties

In addition, there space two special rhombus properties. All 4 sides are equal, and also the diagonals space perpendicular. For this reason if you have actually a parallelogram through perpendicular diagonals, it has to be a rhombus. Ns will point out, though, the is possible to have an irregular quadrilateral that has actually perpendicular diagonals.

That diagonal property is separable indigenous the others. So you could have an rarely often, rarely quadrilateral that doesn’t have the large four, doesn’t have actually the equal sides, however it does have perpendicular diagonals. That residential property alone have the right to be separated native the various other four. It’s not like the huge four properties that constantly come together. Rectangles, rectangles room quadrilaterals with four 90-degree angles.

We could contact them equiangular quadrilaterals. It’s very interesting v a triangle, the just equilateral triangle is equiangular, and the just equiangular triangle is equilateral. Those two constantly have to come together with triangles. Yet we can separate those two once we obtain two quadrilaterals, or come any higher polygons, the you can have the equiangular shape without the it is intended shape.

So rectangles have all same angles. And in a fact, among those rectangles, EFGH, is a golden rectangle. Rectangles are parallelograms, and the huge four parallel properties space true for them. In addition, there room two distinct rectangle properties. Obviously, all four angles room equal to every other and the diagonals room congruent, for this reason QS = PR.

And again, this diagonal property, this have the right to be separated the end from the others. We could have an rarely often, rarely quadrilateral that doesn’t have any type of of the huge four, doesn’t have actually right angles, yet it does have actually congruent diagonals. So the property can be separated out from the various other four. It’s important to appreciate that. Finally, among this set, we’ll talk around squares.

## What’s so Special about Squares?

Squares are the most elite quadrilaterals, the form with the highest variety of special properties. A square is a rectangle, a square is a rhombus, and a square is a parallelogram. Therefore it has all the rectangle properties, every the parallel properties, every the rhombus properties. And so it’s a very, an extremely special shape.

If we are told that a number is a square, now that’s amazing. If the test difficulty actually states this form is a square, they’re offering us a ton that information. And that is a really powerful thing to know. There’s all kinds that geometry facts we understand if we simply have actually the information that a shape is a square.

### Don’t it is in Fooled!

But it’s really hard to prove the something is a square. Don’t be gullible in assuming that a form is a square once you don’t have enough information to do so. The is one really common catch on the test. If the shape is close to gift a square yet not exactly a square, that doesn’t necessarily have any type of of the square properties.

Here are two drawn to scale diagrams. Both of these look prefer squares, yet neither is. So the one top top the left, EFGH, turns out to be a rhombus. The four sides room equal however one angle is slightly less than 90 degrees, the various other angle will certainly be slightly more than 90 degrees. Therefore it’s not specifically a square.

The various other one has three same sides and also then has one next that’s a tiny bit less, KL is a small bit less. That looks like angle M is 90 degrees, however angle K is higher than 90 degrees, and also the other two room slightly less and also unequal to every other. Therefore that’s a entirely irregular quadrilateral. But, drawn to scale, it looks like a square.

Just the reality that even if we have actually something the is attracted to scale and looks favor a square, there’s no guarantee the it is a square.

## Practice Problem

Here’s a practice problem. Stop the video and then we’ll talk around this.

Okay, this is a really odd inquiry format. Can we identify that ABCD is a square if we recognize either the these?

So, BC = CD, and also angle B is 90 degrees. So that’s truth number 1. Advertisement = abdominal muscle and angle D = 90 degrees. And so the inquiry is using simply one of them, have the right to we identify that it’s a square? If we put both of them together, is that enough to recognize that it’s a square? Or if, even if we placed them both together, it’s not enough to prove that something is a square.

Turns out that if also both truth together space true, the does no guarantee that the shape is a square. It might be simply two congruent right triangles attached in ~ the hypotenuse, like this. So in this diagram, the is true the BC = CD, it is true that ad = AB, and also we do have actually right angle at B and also D, and also yet ABCD is not a square.

In fact, it’s not any type of special square at all. All this info is not sufficient to determine that ABCD is a square and the answer to the concern is C.