Properties of Trapezoids and Kites

1
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

2
Figure QRST is a trapezoid

• QR and TS are bases
• ltQ and ltR are base angles
• ltT and ltS are base angles
• QT and RS are legs of trapezoid

Q
R
S
T
3
Midsegment of a trapezoid

• The midsegment of a trapezoid is the segment
  whose endpoints are the midpoints of the legs of
  the trapezoid

4
Theorem 69-1trapezoid 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
• EF is parallel to D
• EF ½(AB DC)

F
E
5
Find the length of EF
E
F
6
Properties of Isosceles Trapezoids

• Base angles of an isosceles trapezoid are
  congruent.
• If trapezoid ABCD is isosceles, then ltA is
  congruent to ltB and ltC is congruent to ltD

7
Properties of Isosceles Trapezoids

• The diagonals of an isosceles trapezoid are
  congruent

8
Properties of Kites

• Kites are quadrilaterals with exactly 2 pairs of
  congruent adjacent sides
• The diagonals of a kite are perpendicular

9
Find the lengths of the sides of the kite
W
4
X
Z
5
5
8
Y
10
practice

• EF is the midsegment of trap ABCD. Find the
  length of CD

22 in.
38 in.
11
Find the measures of the angles in trapezoid
48
12
Find BE

• AC 17.5, AE 9.6

E
13
Find the lengths of the sides of kite to the
nearest tenth
2
7
4
2
14
(No Transcript)