Transcript Properties of Trapezoids and Kites

Properties of Trapezoids and Kites
The bases of a trapezoid are its 2 parallel sides
A base angle of a trapezoid is 1 pair of consecutive
angles whose common side is a base of the trapezoid
Trapezoids have 2 pairs of base angles.
The legs of a trapezoid are the 2 nonparallel sides
Figure QRST is a trapezoid
•
•
•
•
QR and TS are bases
<Q and <R are base angles
<T and <S are base angles
QT and RS are legs of trapezoid
Q
T
R
S
Midsegment of a trapezoid
• The midsegment of a trapezoid is the
segment whose endpoints are the midpoints
of the legs of the trapezoid
Theorem 69-1
trapezoid midsegment theorem
• The midsegment of a trapezoid is parallel to both
bases and has a length that is equal to half the sum
of the bases
• EF is midsegment
• EF is parallel to AB
F
• EF is parallel to D
E
• EF = ½(AB + DC)
Find the length of EF
E
F
Properties of Isosceles Trapezoids
• Base angles of an isosceles trapezoid are
congruent.
• If trapezoid ABCD is isosceles, then <A is
congruent to <B and <C is congruent to <D
Properties of Isosceles Trapezoids
• The diagonals of an isosceles trapezoid are
congruent
Properties of Kites
• Kites are quadrilaterals with exactly 2 pairs of
congruent adjacent sides
• The diagonals of a kite are perpendicular
Find the lengths of the sides of the
kite
W
4
Z
5
5
8
Y
X
practice
• EF is the midsegment of trap ABCD. Find
the length of CD
22 in.
38 in.
Find the measures of the angles in
trapezoid
48
Find BE
• AC = 17.5, AE = 9.6
E
Find the lengths of the sides of kite
to the nearest tenth
2
7
4
2