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

2. Definitions Imagine 2 adjacent isosceles triangles.

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

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

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

6. Definitions

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

8. 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.

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

10. Real Life Connection

12. Book Exercises

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21. Definitions What is a midsegment of a triangle ?

22. EXAMPLES NON-EXAMPLES

23. 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.

24. Definitions What is a midsegment of a triangle ?

25. Definitions What is a midsegment of a trapezoid ?

26. 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?

27. 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.

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44. 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