1. Properties of Trapezoids and Kites Unit 7-4

2. Definitions Trapezoid– a quadrilateral with only one pair of parallel sides.

3. Definitions Bases— bases the parallel sides of a trapezoid are called “bases”.

4. Definitions Legs– legs the non-parallel side of a trapezoid

5. Definitions Midsegment--- Midsegment midpoint 5 13 ?? Midsegment = =9 parallel to both bases. Connects the midpoints of the legs. Its length is equal to half of the sum of the length of the bases midpoint

6. Theorems for Trapezoids If a quadrilateral is an isosceles trapezoid, then both sets of base angles are equal. If one pair of base angles are equal, then the trapezoid is isosceles If a quadrilateral is an isosceles trapezoid, then the diagonals are equal

7. Examples Find the length of Trapezoid PLOT 1. Graph the points PLOT T L O P 2. Find the lengths of both bases TO = 6 PL = 5 3. Use the midsegment formula 5 + 6 / 2 = 5.5

8. Examples AB H F C G E D 27.2 39.2 74 The figure at the right is an isosceles trapezoid. Find the missing measures. m<A = m<B = m<C = m<AEF = m<BHG= 106 o 74 o EF = 33.2 GH= 30.2

9. Rules for Kites If a quadrilateral is a kite, then its diagonals are perpendicular. then exactly one pair of opposite angles are equal then its consecutive sides are equal

10. Rules for Kites C E A B D 1. Diagonals are perpendicular 2. One set of opposite angles are equal 3. Consecutive sides are equal

11. Example for Kites In the kite EFGH GJ = 13 JH = 16 JE = 22 E F G H J Find the perimeter of the kite (tenths) 13 16 22 27.2 16 20.6 Perimeter = 95.6 27.2 20.6

12. Example for Kites In the kite MNPS, m<MSR = 25 o m<MNR = 57 o S M N P R Find the measures m< MRN= m< NMR = m< MRS = m< SMR = m<SPN = 25 o 57 o 33 o 90 o 33 o 90 o 65 o 98 o

13. LAST EXAMPLE of CHAPTER 6  On graph paper……Decide what the shapes are (most specific by properties).  A (-4,-1)  B (-4,6)  C (2,6)  D (2,-4)  M (-5,2)  N (-5,6)  P (-1,6)  R (2,-1)  S (-4,-3)  T (0,3)  V (4,3)  W (8,-3)  F (-2,-2)  G (1,7)  H (4,4)  J (1,-5) Group 1Group 2Group 3Group 4