Name
LESSON
6-6
Date
Class
Reteach
Properties of Kites and Trapezoids
'
A kite is a quadrilateral with exactly two pairs of congruent
consecutive sides. If a quadrilateral is a kite, such as FGHJ,
then it has the following properties.
&
(
*
Properties of Kites
'
_
&
'
_
FH ' GJ
(
&
/G > /J
(
*
*
Exactly one pair of opposite angles is
congruent.
The diagonals are perpendicular.
A trapezoid is a quadrilateral with exactly one pair of parallel sides. If the legs of
a trapezoid are congruent, the trapezoid is an isosceles trapezoid.
BASE
LEG
BASE
Each i side is
called a base.
Each nonparallel side
is called a leg.
Base angles are two
consecutive angles whose
common side is a base.
Isosceles Trapezoid Theorems
• In an isosceles trapezoid, each pair of base angles is congruent.
• If a trapezoid has one pair of congruent base angles, then it is isosceles.
• A trapezoid is isosceles if and only if its diagonals are congruent.
In kite ABCD, m/BCD 5 988, and m/ADE 5 478. Find each measure.
1. m/DAE
"
438
#
2. m/BCE
%
558
3. m/ABC
!
$
708
4. Find m/J in trapezoid JKLM.
+
5. In trapezoid EFGH, FH 5 9. Find AG.
&
,
!
124°
6.2
*
-
%
568
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
46
'
(
2.8
Holt Geometry
Name
Date
Class
Reteach
LESSON
6-6
Properties of Kites and Trapezoids
continued
Trapezoid Midsegment Theorem
The midsegment of a trapezoid is the segment
whose endpoints are the midpoints of the legs.
-
• The midsegment
of a trapezoid
is parallel to
_ _
_ _
each base. AB i MN and AB i LP
• The length of the midsegment is one-half
the sum of the length of the bases.
1 (MN 1 LP )
AB 5 __
2
.
!
"
,
0
_
AB is the
midsegment
of LMNP.
Find each value so that the trapezoid is isosceles.
6. Find the value of x.
7. AC 5 2z 1 9, BD 5 4z 2 3. Find the
value of z.
"
3
2
#
(5X 2 32)°
(7X 2)°
1
!
4
$
z56
x 5 64
Find each length.
8. KL
9. PQ
'
16
26
1
7.5
3
,
+
&
0
(
.
*
5.5
4
2
21
9.5
10. EF
11. WX
#
6
9
%
"
4.3
!
&
14
35
$
5
9.15
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
22.9
7
8
:
10.8
47
Holt Geometry