1. Date: Sec 8-5 Concept: Trapezoids and Kites
Objective: Given properties of trapezoids and kites we will solve problems as measured by a s.g.

2. Trapezoid
A quadrilateral with 1 pair of opposite sides parallel

3. A trapezoid with congruent legs
Isosceles Trapezoid
A trapezoid with congruent legs

4. Properties of Isosceles Trapezoids
Legs of an isosceles trapezoid are congruent
Base angles of an isos. trap. are congruent
Diagonals of an isos trap. are congruent

5. Example: CDEF is an isos. Trap. With CE = 10, and m<E=125°
Find DF _______
m<C _________
m<D _________
m<F _________ D
E = 125° F C 10 55
125 55

6. Midsegment of a TrapezoidB C N D
The midsegment of a trapezoid is parallel to each base and it length is 1/2 the sum of the lengths of the bases
MN=1/2 (BC+AD)

7. Example: Find the length of the midsegment MNB C M N 12 10
MN = 1/2(12+10)
= 1/2(22)
= 11

8. Example: 4 7 x
7 = 1/2(4+x)
14 = 4+x
10 = x

9. A quadrilateral with 2 pairs of consecutive congruent sides
Kites
A quadrilateral with 2 pairs of consecutive congruent sides

10. Properties of Kites There are 2 pairs of consecutive sides congruentx
There are 2 pairs of consecutive sides congruent
There is exactly 1 pair of congruent angles
Diagonals are perpendicular

11. Example: RSTV is a kite. Find m<R___________ m<S___________
m<T___________ 70
m<S=125 since <S and <U are congruent
125
x+x = 360
2x+280=360
2x = 80
x=40 40 T R U S
125
x+30 x
x=40=m<T
x+30 = =70 = m<R

12. Example: GHJK is a kite. Find HP
Since the Diagonals are perpendicular, HPG is right.
You can use the Pythagorean Thm.
a2+b2=c2
42+x2=52
16+x2=25
x2=9
x=3 H J K G 5 4 X P

13. Today's Work