1 / 18

Properties of Trapezoids and Kites

Properties of Trapezoids and Kites. Geometry H2 (Holt 6-6) K. Santos. Kite. Kite—a quadrilateral with exactly two pairs of consecutive sides congruent A B D C. Theorem 6-6-1.

rich
Download Presentation

Properties of Trapezoids and Kites

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Properties of Trapezoids and Kites Geometry H2(Holt 6-6) K. Santos

  2. Kite Kite—a quadrilateral with exactly two pairs of consecutive sides congruent A B D C

  3. Theorem 6-6-1 If a quadrilateral is a kite, then its diagonals are perpendicular. A B D C

  4. Theorem 6-6-2 If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent. A B D C <B <D

  5. Other Kite Observations --adjacent sides congruent --no parallel sides --1 pair opposite angles congruent --diagonals perpendicular --one diagonal bisects angles formed by adjacent sides --one diagonal is bisected --symmetry about one diagonal --two sets of congruent right triangles

  6. Kite Example Find all the missing angles. 50 70

  7. Trapezoid Trapezoid—a quadrilateral with exactly one pair of opposite sides parallel A B D C Bases: parallel sides and Legs: non-parallel sides and

  8. Isosceles Trapezoid Isosceles Trapezoid—a trapezoid with congruent legs (non-parallel sides) A B D C

  9. Theorem 6-6-3 If a quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent. B C A D Given: ABCD is an isosceles trapezoid Then: < B < C < A < D

  10. Theorem 6-6-4 If a trapezoid has one pair of congruent base angles then the trapezoid is isosceles. A D B C Given: < B < C Then: ABCD is an isosceles trapezoid

  11. Theorem 6-6-5 A trapezoid is isosceles if and only it its diagonals are congruent. B C A D Given: ABCD is an isosceles trapezoid Then:

  12. Example—Trapezoid--angles WXYZ is an isosceles trapezoid, m< X = 156. Find m < Y, m < Z and m < W. W Z X Y

  13. Example—Trapezoid--Diagonals AD = 12x -11 and BC = 9x - 2. Find the value of x so that ABCD is an isosceles trapezoid. A B C D

  14. Midsegment of a trapezoid Midsegment of a trapezoid—is the segment whose endpoints are the midpoints of the legs. R S M N U T is the midsegment

  15. Trapezoid Midsegment Theorem (6-6-6) The midsegment of a trapezoid is parallel to each base, and its length is one half the sum of the bases. S T M N R U |||| MN = (average of the parallel bases)

  16. Example--Midsegment Find x. 8 x 14

  17. Example--Midsegment Find EH. F 25 G X 16.5 Y E H

  18. Example—Midsegment (algebraic) Find the length of the midsegment. n + 2 n + 10 3n - 12

More Related