Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "Kite"

m (added links)
m (corrected inaccurate statement)
 
(5 intermediate revisions by 5 users not shown)
Line 1: Line 1:
−
A '''kite''' is a geometric figure that lies in a plane.  [[Quadrilateral]] <math>ABCD</math> is a kite if and only if <math>\overline{AB}=\overline{BC}</math> and <math>\overline{CD}=\overline{DA}</math>.  Thus, there are two types of quadrilateral with a two pairs of [[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 the kite 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]

Definition and Usage

A kite is a geometric figure that lies in a plane. Quadrilateral $ABCD$ is a kite if and only if $AB=BC$ and $CD=DA$ or $AB=AD$ and $BC=CD$. 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:

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=Kite&oldid=223400"