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KITES
By: Henry B., Alex R., Juan M.,
Daniela E., Carolina M.
Period 5
Definition

A kite is a
quadrilateral that
has two pairs of
adjacent sides that
are congruent and
no opposite sides
that are congruent.
Theorem 6-17
• Theorem 6-17
The diagonals of a kite are
perpendicular.
Proof of Theorem 6-17
Given- Kite RSTW with segment TS
congruent to segment TW; Segment
RS is congruent to segment RW
Prove: Segment TR is perpendicular
to segment SW
Proof: Both T and R are equidistant from S
and W. By the Converse of the Perpendicular
Bisector Theorem, T and R lie on the
perpendicular bisector of segment SW. Since
there is exactly one line through any two points
by Postulate 1-1, segment TR must be on the
perpendicular bisector of segment SW.
Therefore, segment TR is perpendicular to
segment SW.
T
S
Z
R
W
Theorem
 If a quadrilateral
is a kite, then
exactly one pair
of opposite
angles is
congruent.
Line of Symmetry

The line passing
through the vertices
of the non congruent
angles is the line of
symmetry.
Line of
symmetry
The End
Investigation 6.3.1 Kites Cont.


Kite Angles Conjecture- The nonvertex angles of a kite are
congruent.
Kite Angle Bisector ConjectureThe vertex angles of a kite are
bisected by a diagonal.
Investigation 6.3.1 Kites


Kite Diagonal Bisector
Conjecture- The diagonal
connecting the vertex angles of a
kite is the perpendicular bisector
of the other diagonal.
Kite Diagonals Conjecture- the
diagonals of a kite are
perpendicular.