Download traps, kites, midsegment thrm

6.5
Trapezoids & Kites
Trapezoid
• Is a quadrilateral with exactly 1 pair of
parallel sides
Trapezoid
A
BASE
C
B
D
BASE
If the legs are congruent then
the trapezoid is an isosceles
trapezoid.
Theorem 6.14
•If a trapezoid is isosceles, then
each pair of base angles is
congruent.
Theorem 6.15
•If a trapezoid has a pair of
congruent base angles, then it is
an isosceles trapezoid.
Theorem 6.16
•A trapezoid is isosceles if and only
if its diagonals are congruent.
Midsegment
•The midsegment of
a trapezoid is the
segment that
connects the
midpoints of its
legs.
THM 6.17
• The midsegment of a
trapezoid is parallel to
each base and its length is
one half the sum of the
lengths of its bases
1
midsegment  base1  base 2 
2
EX 1 Find the length of MN.
P
M
13
S
10
Q
16
N
R
EX 2 Find the value of x.
19
15
17
x
A Kite
• A quadrilateral with
two pairs of
consecutive
congruent sides, but
opposite sides are
not congruent.
Theorem 6.18
•If a quadrilateral is a kite, then its
diagonals are perpendicular.
Theorem 6.19
•If a quadrilateral is a kite, then
exactly one pair of opposite angles
is congruent.
Ex 3 Find the measure of the sides.
Round to the nearest tenth.
L
LM = 3.6
LO = 3.6
ON= 5
MN = 5
2
O
3
3
4
N
M
Ex 4 Find the mL.
L
110
M
100
40
O
N
Ex 5 Find the mL.
L
35
M
x
O
55
135
N
Add Trapezoid and
Kite to your
foldable.
Goal: Identify midsegments and use properties of
midsegments of a triangle
Midsegment – a
segment that connects
the midpoints of two
sides of a triangle.
Midsegment Theorem
The segment connecting the
midpoints of two sides of a
triangle is parallel to the
third side and half as long.
X
B
Y
AC || XY
XY = ½ AC
A
C
Ex 1: UW and VW are midsegments of
RST. Find UW and RT.
R
U
UW = 6
RT = 16
V
12
8
T
W
S
Ex 2: X, Y, and Z are the midpoints of UVW.
Complete each statement.
a. If VW = 6a, then XY = ___
U
c. XZ  _______.
X
V
b. mWZY = 2b + 1, then
mWVU = ______.
Y
Z
d. If YZ = c, then UV = ____
W