Question 1019302: Here is the question
http://prntscr.com/a217yn
So, I found the slopes of each side.
CD=3/0
CB=0/3
BA=4
AD=1/4
However, this doesn't answer my question. I'm pretty sure it's a kite, but for me to say it's a quite I have to prove the diagonals are perpendicular or I have to prove the consecutive sides are congruent with no parallel sides congruent (meaning just proving the consecutive sides are congruent).
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your problem statement is shown here:
http://prntscr.com/a217yn
the properties of a kite are:
In a kite,
1. Two disjoint pairs of consecutive sides are congruent by definition.
2. The diagonals are perpendicular.
3. One diagonal is the perpendicular bisector of the other.
4. One of the diagonals bisects a pair of opposite angles.
5. One pair of opposite angles are congruent.
if you can show that all of these properties are true, then what you have is a kite.
you can label your points as shown below:
A = (2,6)
B = (5,6)
C = (5,3)
D = (1,2)
i labeled point E as the midpoint of AC.
here's a reference from dummies.com.
http://www.dummies.com/how-to/content/how-to-prove-that-a-quadrilateral-is-a-kite.html
dummies.com claims the following:
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Proving that a quadrilateral is a kite is a piece of cake. Usually, all you have to do is use congruent triangles or isosceles triangles. Here are the two methods:
If two disjoint pairs of consecutive sides of a quadrilateral are congruent, then it’s a kite (reverse of the kite definition).
If one of the diagonals of a quadrilateral is the perpendicular bisector of the other, then it’s a kite (converse of a property).
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so, either one of those definitions should be sufficient, if i can assume that dummies is correct.
to prove these, here's what you need to do.
number 1:
If two disjoint pairs of consecutive sides of a quadrilateral are congruent, then it’s a kite (reverse of the kite definition).
show that AB = BC and AD = CD
number 2:
If one of the diagonals of a quadrilateral is the perpendicular bisector of the other, then it’s a kite.
show that the slope of BD is the negative reciprocal of the slope of AC.
this proves they are perpendicular to each other.
show that the midpoint of AC is equal to point E.
that means that AE is congruent to EC which means that BD is the perpendicular bisector of AC.
my diagram of your kit is shown below with the points labeled.
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