Kites Trapezoids Midsegments Geometry Regular Program SY 2014

Definitions Imagine 2 adjacent isosceles triangles.

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

Kite Properties Kite Angle Bisector Conjecture: The vertex angles of a kite are bisected

Kite Properties Kite Diagonal Bisector Conjecture: The diagonal connecting the vertex angles of a

Trapezoid Properties Trapezoid Consecutive Angles Conjecture: In a trapezoid, the consecutive angles between the

Trapezoid Properties Isosceles Trapezoid Conjecture: In an isosceles trapezoid, the base angles are congruent.

Trapezoid Properties Isosceles Trapezoid Diagonals Conjecture: In an isosceles trapezoid, the diagonals are congruent.

Book Exercises Answer the following: p. 271

Definitions What is a midsegment of a triangle ?

Definitions What is a midsegment of a triangle ? A midsegment of a triangle

Definitions What is a midsegment of a trapezoid ?

Definitions What is a midsegment of a trapezoid ? A midsegment of a trapezoid

Midsegment Properties Triangle Midsegment Conjecture: In a triangle, the midsegment is parallel to the

Book Exercises Answer the following: p. 277

MORE Exercises Answer the following: p. 304

MORE Exercises ALWAYS. SOMETIMES. NEVER. 1. The diagonals of a kite are congruent. N

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Kites, Trapezoids, Midsegments Geometry Regular Program SY 2014 -2015 Source: Discovering Geometry (2008) by Michael Serra

Definitions Imagine 2 adjacent isosceles triangles.

Kite Properties Kite Angles Conjecture: The non-vertex angles of a kite are congruent. Kite Diagonals Conjecture: The diagonals of a kite are perpendicular. A M T H

Kite Properties Kite Angle Bisector Conjecture: The vertex angles of a kite are bisected by a diagonal. A M T H

Kite Properties Kite Diagonal Bisector Conjecture: The diagonal connecting the vertex angles of a kite is the perpendicular bisector of the other diagonal. A M T H

Definitions

Trapezoid Properties Trapezoid Consecutive Angles Conjecture: In a trapezoid, the consecutive angles between the bases are supplementary.

Trapezoid Properties Isosceles Trapezoid Conjecture: In an isosceles trapezoid, the base angles are congruent. *Converse of Isosceles Trapezoid Conjecture: In a trapezoid, if the base angles are congruent, then the trapezoid is isosceles.

Trapezoid Properties Isosceles Trapezoid Diagonals Conjecture: In an isosceles trapezoid, the diagonals are congruent.

Real Life Connection

Book Exercises

Book Exercises Answer the following: p. 271

Definitions What is a midsegment of a triangle ?

EXAMPLES NON-EXAMPLES

Definitions What is a midsegment of a triangle ? A midsegment of a triangle is… a segment whose endpoints are the midpoints of two sides of a triangle.

Definitions What is a midsegment of a triangle ?

Definitions What is a midsegment of a trapezoid ?

Definitions What is a midsegment of a trapezoid ? A midsegment of a trapezoid is… a segment whose endpoints are the midpoints of the non-parallel sides (legs) of a trapezoid. Can you draw non-examples of a midsegment of a trapezoid?

Midsegment Properties Triangle Midsegment Conjecture: In a triangle, the midsegment is parallel to the third side, and measures half the length of the third side. Trapezoid Midsegment Conjecture: In a trapezoid, the midsegment is parallel to the bases, and measures half the sum of the lengths of the bases.

Book Exercises Answer the following: p. 277

MORE Exercises Answer the following: p. 304

MORE Exercises ALWAYS. SOMETIMES. NEVER. 1. The diagonals of a kite are congruent. N 2. Consecutive angles of a kite are supplementary. N 3. The diagonal connecting the vertex angles of a kite divides the kite into two congruent triangles. A 4. The diagonals of a trapezoid bisect each other. N 5. The three midsegments of a triangle divide the triangle into 4 congruent triangles. A 6. The midsegment of a trapezoid is perpendicular to a leg of the trapezoid. S