8.5 Kites & Trapezoids.

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Presentation transcript:

8.5 Kites & Trapezoids

Proving Kite Properties Kite Non-vertex Angles Thm The non-vertex angles of a kite are congruent. Kite Angle Bisector Thm The vertex angles of a kite are bisected by a diagonal. Kite Diagonals Thm The diagonals of a kite are perpendicular. Kite Diagonal Bisector Thm The diagonal connecting the vertex angles of a kite is the perpendicular bisector of the other diagonal.

Proving Trapezoid Properties Trapezoid Consecutive Angles Thm The consecutive angles between the bases of a trapezoid are supplementary. Isosceles Trapezoid Thm The base angles of an isosceles trapezoid are congruent. Converse Isosceles Trapezoid Diagonals Thm A trapezoid is isosceles if and only if its diagonals are congruent.

Examples (Discovering Geometry by Serra) 3 6 12 Determine the perimeter. 1. z 2.

Examples (Discovering Geometry by Serra) 4. 3.

Exercises (p. 540, Larson)

Midsegments 5.1 of a Triangle 8.5 of a Trapezoid

The 3 midsegments of a triangle divide it into 4 congruent triangles.

Examples (p.297, Larson)

Exercises (Discovering Geometry by Serra) 12 z 2. 1. 3. 4. 5.

Exercises (Discovering Geometry by Serra) 6. 8. 7.

Exercises (p.540, Larson)

In Summary (pp.544 - 549, Larson)

In Summary (pp.544 - 549, Larson)

In Summary (pp.544 - 549, Larson)

In Summary (pp.544 - 549, Larson)

In Summary (pp.544 - 549, Larson)

In Summary (pp.544 - 549, Larson)

In Summary (pp.544 - 549, Larson)

In Summary (pp.544 - 549, Larson)

In Summary (pp.544 - 549, Larson)