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Kites, Trapezoids, Midsegments

Explore the properties and conjectures of kites and trapezoids, including angles, diagonals, midsegments, and real-life connections. Learn from AMTH definitions and book exercises. Understand midsegments in triangles and trapezoids. Answer exercises to deepen your understanding.

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Kites, Trapezoids, Midsegments

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  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. A M T H

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

  11. Real Life Connection

  12. Book Exercises

  13. Book Exercises Answer the following: p. 271

  14. Book Exercises Answer the following: p. 271

  15. Book Exercises Answer the following: p. 271

  16. Book Exercises Answer the following: p. 271

  17. Book Exercises Answer the following: p. 271

  18. Book Exercises Answer the following: p. 271

  19. Book Exercises Answer the following: p. 271

  20. Book Exercises Answer the following: p. 271

  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.

  28. Book Exercises Answer the following: p. 277

  29. Book Exercises Answer the following: p. 277

  30. Book Exercises Answer the following: p. 277

  31. Book Exercises Answer the following: p. 277

  32. Book Exercises Answer the following: p. 277

  33. Book Exercises Answer the following: p. 277

  34. Book Exercises Answer the following: p. 277

  35. Book Exercises Answer the following: p. 277

  36. Book Exercises Answer the following: p. 277

  37. MORE Exercises Answer the following: p. 304

  38. MORE Exercises Answer the following: p. 304

  39. MORE Exercises Answer the following: p. 304

  40. MORE Exercises Answer the following: p. 304

  41. MORE Exercises Answer the following: p. 304

  42. MORE Exercises Answer the following: p. 304

  43. MORE Exercises Answer the following: p. 304

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

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