1. KITES By: Henry B., Alex R., Juan M., Daniela E., Carolina M. Period 5

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

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

4. Proof of Theorem 6-17 W T S R Z 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.

5. Theorem  If a quadrilateral is a kite, then exactly one pair of opposite angles is congruent.

6. Line of Symmetry The line passing through the vertices of the non congruent angles is the line of symmetry. Line of symmetry

7. The End

8. Investigation 6.3.1 Kites Cont. Kite Angles Conjecture- The non- vertex angles of a kite are congruent. 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. Kite Angle Bisector Conjecture- The vertex angles of a kite are bisected by a diagonal.

9. 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 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. Kite Diagonals Conjecture- the diagonals of a kite are perpendicular.