KITES

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KITES

• By Henry B., Alex R., Juan M., Daniela E.,
  Carolina M.
• Period 5

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Definition

• A kite is a quadrilateral that has two pairs of
  adjacent sides that are congruent and no opposite
  sides that are congruent.

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Theorem 6-17

• Theorem 6-17
• The diagonals of a kite are perpendicular.

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Proof of Theorem 6-17
Given- Kite RSTW with segment TS congruent to
segment TW Segment RS is congruent to segment RW
T
W
S
Prove Segment TR is perpendicular to segment SW
Z
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.
R
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Theorem

• If a quadrilateral is a kite, then exactly one
  pair of opposite angles is congruent.

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Line of Symmetry

• The line passing through the vertices of the non
  congruent angles is the line of symmetry.

Line of symmetry
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The End
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Investigation 6.3.1 Kites Cont.

• Kite Angles Conjecture- The non-vertex angles of
  a kite are congruent.
• Kite Angle Bisector Conjecture- The vertex angles
  of a kite are bisected by a diagonal.

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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.