KITES

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

DefinitionDefinition

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

Theorem 6-17Theorem 6-17

• Theorem 6-17

The diagonals of a kite are perpendicular.

Proof of Theorem 6-17Proof 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.

Theorem Theorem

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

Line of Symmetry The line passing

through the vertices of the non congruent angles is the line of symmetry.

Line of symmetry

The EndThe End

Investigation 6.3.1 Kites Cont.Investigation 6.3.1 Kites Cont.

Kite Angles Conjecture-Kite Angles Conjecture- The non- The non-vertex angles of a kite are vertex angles of a kite are congruent.congruent.

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

Investigation 6.3.1 KitesInvestigation 6.3.1 Kites

Kite Diagonal Bisector Kite Diagonal Bisector Conjecture-Conjecture- The diagonal The diagonal connecting the vertex angles of a connecting the vertex angles of a kite is the perpendicular bisector kite is the perpendicular bisector of the other diagonal.of the other diagonal.

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