Classifying geometric shapes
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Which of the following names can be used to describe the geometric shape below? So the first name in question is a quadrilateral. And a quadrilateral is literally any closed shape that has four sides. And this is definitely a closed shape that has four sides. So it is definitely a quadrilateral. Next, we have to think about whether it is a parallelogram. A parallelogram is a quadrilateral that has two pairs of parallel sides, where in each pair they're opposite sides. And in this case, if you look at this side over here, it forms a 90-degree angle with this line. And this side over here also forms a 90-degree angle with this line over here. So these two sides are parallel. And then you could make the exact same argument for the other two sides. This line up here forms a 90-degree angle with this side. And so does this side. It forms a 90-degree angle with this line right over here. They form the same angle with this line. They're parallel. So this side is parallel to that side right over there. So this is definitely also a parallelogram. Next, we ask about a trapezoid. Now, trapezoid is interesting. Sometimes a trapezoid is defined as any quadrilateral having at least one pair of parallel sides. Sometimes it's defined as having only one pair of parallel sides. So let me write this down. Trapezoid, there's a debate here. It's not completely settled. Some people say at least one pair of parallel sides. That's one definition, one possible definition. The other one is at exactly one pair of parallel sides. How we answer this question depends on which definition for trapezoid we pick. Now, the one that people most refer to is actually this one right over here, exactly one pair of parallel sides. So when you think of a trapezoid, they think of something like this, where this side over here is parallel to that side over here and those two are not parallel. But sometimes you'll also see this at least one pair of parallel sides. And so this would include parallelograms. It would be inclusive of parallelograms because parallelograms have two pairs of parallel sides. But I'm going to go with this definition right over here, exactly one pair of parallel sides. This has two pairs of parallel sides so I will not call it a trapezoid. But it's always important to clarify what people are talking about because some people might say a trapezoid is at least one pair of parallel sides. And if we used that definition, then we would call it a trapezoid. So it really depends on the definition that you're using. Now, let's go on to rhombus. So a rhombus is a quadrilateral where four of the sides are congruent. So a rhombus will look like this. All four sides have the same length. They're not necessarily at right angles to each other. This figure over here, we have two pairs of a size that are the same length, but there's no information that tells us that this side is equal to that side or that this side is equal to that side. So we can't make the claim that this is necessarily a rhombus. We don't know for sure. If someone told us that this length is equal to that length, then things change. But for the sake of this one, we're not going to go with a rhombus. A rectangle is essentially a parallelogram that has four right angles. And we already established this is a parallelogram, and it also has four right angles-- one, two, three, four. So this is a rectangle. Another way to think about a rectangle is opposite sides have the same length, and you have four right angles. So this is definitely a rectangle. A square, a couple of way you can think about a square. You could view a square as a rhombus with four right angles . So if were to straighten it out a little bit, it's a rhombus so all the four sides are the same. And you have four right angles. That's one way to think about a square. Or you could view it as a rectangle where all four sides are congruent. But in either case, you have to have all four sides be congruent in order to be a square. And we already established we ruled out this being a rhombus, that all four sides here are not necessarily congruent. You have two pairs of congruent sides, but we don't know whether this side and this side are congruent. So we cannot call this a square. So it's not a square, not a rhombus, not a trapezoid by the definition we picked, which is the less inclusive version where you say exactly one pair of parallel sides. It is a quadrilateral. It is a parallelogram. It is a rectangle.