Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school
Brian was a geometry teacher through the Teach for America program and started the geometry program at his school
Knowing the properties of a kite will help when solving problems with missing sides and angles. Kite properties include (1) two pairs of consecutive, congruent sides, (2) congruent non-vertex angles and (3) perpendicular diagonals. Other important polygon properties to be familiar with include trapezoid properties, parallelogram properties, rhombus properties, and rectangle and square properties.
There are a couple of key facts about kites
that will help you solve problems
when you have missing sides
or missing angles.
The first key part about how to identify a
kite is you have two pairs of consecutive
congruent sides.
Not opposite like in a parallelogram
or a rectangle.
Notice, we have two consecutive sides
here and they're both congruent.
But these two sides are not
congruent to this pair.
That's the first key thing about a kite.
The second key thing is the nonvertex
angles are congruent.
So if you want to call this angle a vertex
angle, and this angle a vertex angle,
then these two non-vertex angles
will always be congruent.
The third key thing is that the
diagonals are perpendicular.
So if I drew in a diagonal between the vertices
and between the nonvertex angles,
these two will intersect
at a 90-degree angle.
Another key fact about this is that this
diagonal between the two non-vertex
angles is bisected by
this longer diagonal.
So a couple key things to remember when
you are trying to solve problems that
involve a kite.
And one other thing that I forgot to mention
is that this vertex angle is bisected
by this diagonal.
This vertex angle is also bisected but not
necessarily congruent to this angle.
So a lot going on in a kite.
We've got diagonals that are
perpendicular to each other.
This diagonal was bisected, the angles
in the vertex are bisected, and we've
got two pairs of consecutive
congruent sides.
