6.5 Trapezoids
A Trapezoid - a quadrilateral with:
*one pair of parallel sides (called bases)
*two pairs of base angles
*one pair of nonparallel sides (called legs)
If legs are congruent – isosceles trapezoid
B
A
C
D
Ex 1: Given Trapezoid ABCD with BC AD ,
identify the segments or angles as bases,
consecutive sides, legs, diagonals, base
angles, or opposite angles.
C
B
c) AB, BC consecutive
sides
A
a) BC, AD bases
b) BA, CD legs
D d) BD, AC
e)A, C
diagonals
opposite
angles
f)B, C base angles
Thm 6.14 – If a trapezoid is isosceles, then
each pair of base angles is congruent.
B
C
A
D
Thm 6.15 – If a trapezoid has a pair of
congruent base angles, then it is isosceles.
B
A
C
D
Thm 6.16 – A trapezoid is isosceles iff its
diagonals are congruent.
B
A
C
D
If AC  BD , then Trapezoid ABCD is isosceles.
Ex 2: Given isosceles trapezoid PQRS, find
mP, mQ and m R .
S
R
50°
P
Q
The trapezoid is isosceles, so base angles are congruent
(the measures are equal). mR  mS  50 
S , P
are consecutive, hence supplementary.
Ex 2: Given isosceles trapezoid PQRS, find
mP, mQ and m R .
S
R
50°
P
mS  mP  180
50  mP  180
mP  130
Q
Again, base angles
in an isosceles trap
are congruent!
mQ  mP  130
Recall, the midsegment of a triangle joins the
midpoints of the sides. For a trapezoid, it
joins the midpoints of the trapezoid’s legs.
midsegment
Click on the link. Read up to the formula to
determine the length of a trapezoid’s midsegment:
http://www.mathopenref.com/trapezoidmedian.html
Proceed with the PowerPoint when finished.
Ex 3: Find the
length of
midsegment AB .
N
8m
A
M
1
AB  ( NO  MP )
2
1
AB  (8  20)
2
1
AB  ( 28)
2
AB  14m
O
B
20m
P
Ex 4: Find x.
A
E
D
8
B
9
F
x
C
1
EF  ( AB  DC )
2
1
9  (8  x )
Multiply both sides by 2 to
2
get rid of the fraction
18  8  x
10  x  DC
Assignment
Page 359 #10 – 24
*ask for your handout on 6.5 once
you’ve gotten to this slide