Difference between revisions of "Kite"
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| − | A '''kite''' is a geometric figure that lies in a plane. [[Quadrilateral]] <math>ABCD</math> is a kite if and only if <math>AB=BC</math> and <math>CD=DA</math>. Thus, there are two types of quadrilaterals with two pairs of [[congruent (geometry) | congruent]] [[edge]]s, the [[parallelogram]] (if the members of each pair are opposite each other), and the kite (if the members of each pair are adjacent to each other). The properties of kites include: | + | ==Diagram== |
| + | <asy> | ||
| + | dot((0,0)); | ||
| + | dot((-3,5)); | ||
| + | dot((3,5)); | ||
| + | dot((0,7)); | ||
| + | draw((0,0)--(-3,5)--(0,7)--(3,5)--cycle); | ||
| + | </asy> | ||
| + | ==Definition and Usage== | ||
| + | A '''kite''' is a geometric figure that lies in a plane. [[Quadrilateral]] <math>ABCD</math> is a kite if and only if <math>AB=BC</math> and <math>CD=DA</math> or <math>AB=AD</math> and <math>BC=CD</math>. Thus, there are two types of quadrilaterals with two pairs of [[congruent (geometry) | congruent]] [[edge]]s, the [[parallelogram]] (if the members of each pair are opposite each other), and the kite (if the members of each pair are adjacent to each other). The properties of kites include: | ||
* 2 sets of consecutive, congruent sides | * 2 sets of consecutive, congruent sides | ||
* [[perpendicular]] [[diagonal]]s | * [[perpendicular]] [[diagonal]]s | ||
* one pair of opposite, congruent [[angle]]s | * one pair of opposite, congruent [[angle]]s | ||
| + | |||
| + | [[Category:Geometry]] | ||
Latest revision as of 12:09, 22 July 2024
Diagram
![[asy] dot((0,0)); dot((-3,5)); dot((3,5)); dot((0,7)); draw((0,0)--(-3,5)--(0,7)--(3,5)--cycle); [/asy]](http://latex.artofproblemsolving.com/a/0/4/a046c0330eb9e6f943021401c9e3fcb7849b918a.png)
Definition and Usage
A kite is a geometric figure that lies in a plane. Quadrilateral 
is a kite if and only if 
and 
or 
and 
. Thus, there are two types of quadrilaterals with two pairs of congruent edges, the parallelogram (if the members of each pair are opposite each other), and the kite (if the members of each pair are adjacent to each other). The properties of kites include:
- 2 sets of consecutive, congruent sides
- perpendicular diagonals
- one pair of opposite, congruent angles
