Parallelograms
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Parallelograms Document Transcript

  • 1. TRAPEZOIDS, KITES, AND OTHER SPECIAL QUADRILATERALS 1
  • 2. TRAPEZOIDS ‐ a quadrilateral with exactly one pair of parallel sides base leg legBase Angles base ISOSCELES TRAPEZOIDS WOULD HAVE ____________ LEGS 2
  • 3. ISOSCELES TRAPEZOIDS1. If a trapezoid is isosceles, then each pair of base angles is congruent. 2. If a trapezoid has a pair of congruent base angles, then it is an isosceles trapezoid. 3. A trapezoid is isosceles if and only if its diagonals are congruent. 3
  • 4. 500 FIND THE OTHER THREE ANGLES Quadrilaterals interior angles add to... 4
  • 5. Show that quadrilateral ADCB is an isosceles trapezoid. Ask yourself, what are the mandatory A characteristics for an isosceles trapezoid?B D C 5
  • 6. Show that quadrilateral ADCB is a trapezoid. C Ask yourself, what are the mandatory characteristics for a trapezoid?B D A 6
  • 7. B C M MIDSEGMENT (only of the legs) N A DMIDSEGMENT THEOREM FOR TRAPEZOIDSMN = (1/2)(AD + BC) 7
  • 8. B 22 C E F A D 50FIND EF 8
  • 9. KITE‐ a quadrilateral that has two pairs of consecutive congruent sides,but opposite sides are not congruent Diagonals are perpendicular One pair of opposite angles are ≅ 9
  • 10. Xthe figure is a kite 12 Y 20 14 W 12 ZFIND WXFIND XY 10
  • 11. Find the other angles if this figure is a kite1320 600 11
  • 12. √29 5Find the RED side 12
  • 13. SPECIAL QUADRILATERALSWHAT WEVE DONE SO FAR... KNOW THIS! QUADRILATERAL KITE PARALLELOGRAM TRAPEZOID RHOMBUS RECTANGLE ISOSCELES TRAPEZOID SQUARE 13
  • 14. QUADRILATERALKITE PARALLELOGRAM TRAPEZOID TRUE / FALSE RHOMBUS RECTANGLE ISOSCELES TRAPEZOID SQUARE1. A square is a parallelogram 5. A rhombus is a rectangle2. A kite is a trapezoid 6. A square is a rhombus3. A rectangle is a square 7. A rhombus is a square4. An isosceles trapezoid is a 8. A quadrilateral is a rectanglequadrilateral 14
  • 15. Quadrilateral ABCD has at least one pair of opposite sides congruent. What kinds of quadrilaterals meet this condition?PARALLELOGRAM RECTANGLE ISOSCELES TRAPEZOID SQUARE RHOMBUS TRAPEZOID 15
  • 16. THE DIAGONALS OF RSTQ ARE PERPENDICULAR.WHAT QUADRILATERALS MEET THIS CONDITION? 16
  • 17. Join the midpoints of the sides of any quadrilateral, what special quadrilateral is formed? 17
  • 18. What type of quadrilateral is this? 0 120 EXPLAIN 1200600 600 18
  • 19. IN QUADRILATERAL RSTV, m<R = 880, m<S = 1130, AND m<V = 1130.WHAT TYPE OF QUADRILATERAL COULD RSTV BE? EXPLAIN 19
  • 20. THE DIAGONALS OF ABCD INTERSECT AT POINT N TO FORM FOUR ≅ ISOSCELES ΔS: ΔANB ≅ ΔCNB ≅ ΔCND ≅ ΔAND. WHAT TYPE OF QUADRILATERAL IS ABCD? EXPLAIN. 20
  • 21. WAYS TO SHOW A FIGURE IS A RHOMBUS:1. All four sides of the quadrilateral arecongruent2. Quadrilateral is a parallelogram and thediagonals are perpendicular3. Quadrilateral is a parallelogram and thateach diagonal bisects a pair of oppositeangles 21
  • 22. SHOW the figure is rhombus... K(2, 5)L(‐2, 3) N(6, 3) M(2, 1) 22
  • 23. PROPERTY Both pairs of opp.  sides are || Exactly 1 pair of opp. sides are || Diagonals are  perpendicular Diagonals are ≅ Diagonals bisect  each other  23
  • 24. HOMEWORK TEST MONDAY BACK WORK DEADLINE THIS FRIDAY (3/13) NB30Pg. 359 ‐ 362 #s 16 ‐ 24 even, 32 ‐ 36 even (graph paper needed) Pg. 367 ‐ 370 #s 8 ‐ 13, 16 ‐ 24 even, 36 (graph paper needed), 51 24