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# Quadrilateral properties

CCSS.Math:

## Video transcript

which of the following names can be used to describe the geometric shape below so the first name in question is a quadrilateral in 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 the 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 these two sides are parallel and then you can make the exact same argument for the other two sides this line up here forms a 90 degree angle with the side and so does this side forms a 90 degree angle with this line right over here they same 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 asked about a trapezoid now trapezoid is interesting sometimes the trapezoid is defined as any quadrilateral having at least one pair of parallel sides sometimes it's defined it as having only one pair of parallel sides so let me write this down trapezoid there's a debate here no one has it's not completely settled some people say at least at least one pair of parallel parallel sides that's one definition one possible definition the other is the other one is at exactly exactly one pair of parallel sides and this becomes which definition you pick actually it depends how we answer this question depends on which definition for a trapezoid we pick now the one that people most refer to as actually this one right over here exactly one pair of parallel sides so the the trapezoid that most people when you think of a trapezoid they think of something 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 the disc definition right over here exactly one pair of parallel sides this has two pairs of parallel sides so I will not call it I will not call it a trapezoid but you're 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 four of the sides are congruent so a rhombus a rhombus will look like this all four sides 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 sides 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 we're not going to go with rhombus 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 ways you can think about a square you could view a square as a rhombus with four right angles so if you were to kind of straighten it out a little bit it's a rhombus of all the four sides 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 when we ruled out it 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 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 more the less inclusive version where you say exactly one pair of parallel sides it is a Quadra quadrilateral it is a parallelogram it is a rectangle