Properties of Trapezoids and Kites Unit 7-4

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

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

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

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

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

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 / 2 = 5.5

Examples AB H F C G E D 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

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

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

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) Perimeter =

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

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