6.5 trapezoids a trapezoid - a quadrilateral with: *one pair of parallel sides (called bases) *two...
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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
A D
B C
Ex 1: Given Trapezoid ABCD with , identify the segments or angles as bases, consecutive sides, legs, diagonals, base
angles, or opposite angles.
ADBC
ADBC,
BCAB,
CB ,
CA ,
CDBA,
ACBD,A D
B C
a)
b)
c)
d)
e)
f)
bases
legs
consecutive sides
diagonals
opposite angles
base angles
Thm 6.14 – If a trapezoid is isosceles, then each pair of base angles is congruent.
Thm 6.15 – If a trapezoid has a pair of congruent base angles, then it is isosceles.
A D
B C
A D
B C
Thm 6.16 – A trapezoid is isosceles iff its diagonals are congruent.
A D
B C
If , then Trapezoid ABCD is isosceles.BDAC
Ex 2: Given isosceles trapezoid PQRS, findand .,Pm Qm Rm
QP
S R50°
The trapezoid is isosceles, so base angles are congruent (the measures are equal). 50SmRm
are consecutive, hence supplementary.PS ,
Ex 2: Given isosceles trapezoid PQRS, findand .,Pm Qm Rm
QP
S R50°
130
18050
180
Pm
Pm
PmSm
130 PmQm
Again, base angles in an isosceles trap are congruent!
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
P
N
A
M
8m
B
O
20m
mAB
AB
AB
MPNOAB
14
)28(2
1
)208(2
1
)(2
1
Ex 4: Find x.
C
BA
F
8
D
E 9
x
DCx
x
x
DCABEF
10
818
)8(2
19
)(2
1
Multiply both sides by 2 to get rid of the fraction
Assignment
Page 359 #10 – 24
*ask for your handout on 6.5 once you’ve gotten to this slide