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## Geometry (FL B.E.S.T.)

### Course: Geometry (FL B.E.S.T.)>Unit 5

Lesson 6: Parallel & perpendicular lines on the coordinate plane

# Classifying quadrilaterals on the coordinate plane

Watch Sal classify a quadrilateral as a square, rhombus, rectangle, parallelogram, or trapezoid given its four vertices. Created by Sal Khan.

## Want to join the conversation?

• Is there anyway of verifying the angles on the coordinate plane? For example, you draw something that looks like a rectangle, but you can't determine if it is a rectangle or a parallelogram. You determine the sides are parallel by checking the slopes. You verify the distances between the sides are the same by using the distance formula. How do you verify if the angles between are 90 degrees or some other measurement?
• Why did he use delta for "change" in the formula for the slope of a line?
• The capital delta is a standard notation for the change in a variable, and it is used primarily in calculus (and sometimes in those disciplines leading up to it).
• When proving that a Quadrilateral is a parallelogram, can I just prove that one pair of sides are parallel and one distinct pair of sides are congruent? or do I have to prove that both pairs of sides are parallel and congruent?
• It all depends on what you really mean by distinct pairs of sides, IF you have two sides that are parallel and congruent, then that is enough to prove congruency, the other two sides must also be parallel and congruent. But if the "top" and "bottom" sides are parallel, and the left and right sides are congruent, it could either be a parallelogram or a isosceles trapezoid.
• What is the best way to do an exercise like this without the use of a visual coordinate plane to draw on? Is there an "All-Numbers" way of solving this problem?
• Sketching the drawing also helps avoid errors such as finding distances and slope of pairs of points that are diagonals as opposed to sides of the quadrilateral.
• At , why would I need to see if the sides are parallel to each other?
• To know if any of the "shapes" are the right answer. And to know for sure that what you think is right
• what kind of quadrilateral would it be than?
• At , why would it not be a parallelogram or trapezoid?
• It's none of the above. It is just a quadrilateral and not one of the special ones mentioned above, because it does not fulfill any of their constraints:

Parallelogram -> 2 pairs of parallel sides
Trapezoid -> Exactly 1 pair of parallel sides
Rectangle -> 4 right angles
Rhombus -> 4 equal sides
Square -> 4 equal sides and 4 right angles

• Sal used the slope formula to help identify the type of quadrilateral in this video. How could you use other coordinate methods--such as the distance and midpoint formulas--to classify other quadrilaterals? Thank you!
• It was obvious from the diagram that it was none of the quadrilaterals listed. I am not sure how midpoint formula would have any meaning, but it you found the length of the lines by distance formula (or Pythagorean Theorem), the only thing you could know for sure is that if both pairs of opposite sides are equal length, then it must be a parallelogram (or rhombus if all sides are equal). Side lengths would not say anything about a trapezoid. Then you would have to check slopes to see if you could get a more precise answer. By doing slopes, you get a little more information such as a trapezoid if only one set of opposite slopes are the same, at least a parallelogram if both sets of opposite slopes are the same, or at least a rectangle if adjacent slopes are perpendicular (negative reciprocal). So you get more info with slopes, but if you find it is at least a parallelogram or rectangle, you have to go to distance formulas to check and see if there are more precise quad answers.
• At the end of the video, Sal said that it is "none of the above". Wouldn't trapezoid be the answer? (Side AB is parallel to side CD)
(1 vote)
• Unfortunately, sides AB and CD are not parallel. You can confirm that if you find the slope from points AB and the slope from points CD. They are not equal which tells you the line segements are not parallel. Thus, Sal's selection of "none of the above" is correct.

If the line segments had been parallel, then he would have selected the option for Trapezoid.
• How do you draw the conclusion with the slopes you found one the first figure