Download Warm up on a little piece of paper:

Warm up:
Identify the best name for the given traits of
each quadrilateral.
1.) ABCD has two sets of parallel sides and a
right angle.
2.) HGDT has 2 sets of opposite congruent sides
and the left side is congruent to the top
3.) YHBG has 2 sets of opposite congruent angles
and its diagonals are perpendicular.
6.5 TRAPEZOIDS AND
KITES
LEQ: What are the special properties of trapezoids
and kites?
Using properties of trapezoids
Theorem 6-15
 If a trapezoid is
isosceles, then
each pair of base
angles is congruent.
 A ≅ B, C ≅ D C
A
B
D
Proof of part of thm. 6-15
Prove that m<C=m<D
A
B
Construct BE so that it’s
parallel to AC
1
C
1.) AC=BD, AB//CD
1.) Given
2.) AC=BE
2.) Opposite sides of parallelograms are congruent
3.) BE=BD
3.) Transitive Property/substitution
4.) m<D=m<1
4.) Isosceles Triangle Thm.
5.) m<1=m<C
5.) Corresponding Angles
6.) m<C=m<D
6.) Transitive/Substitution
E
D
Ex. 1: Using properties of Isosceles Trapezoids

PQRS is an isosceles
trapezoid. Find mS,
mQ, mR and QR.
P
Q
50°
2.6
S
R

LAYER CAKE A baker is
making a cake like the one
at the right. The top layer
has a diameter of 8 inches
and the bottom layer has a
diameter of 20 inches. How
big should the middle layer
be? (the top of the middle
layer must be exactly
halfway between the top of
the first and 3rd layers)
Recall midsegment of a triangle

Half the distance of the base
Theorem 6-18: Midsegment of a trapezoid

Different!! The median of a
trapezoid is the segment
that connects the
midpoints of its legs. Thm
6-18 says the median:
Is parallel to each
base: MN║AD,
MN║BC
 Has a length equal to
the average of the
base lengths
MN = ½ (AD + BC)
B
M
C
N

A
D
Example: Both are medians
Find the value of x.

Find the value of x.
4
x
5.8
x+3
8.6
22
Theorem 6-16
The diagonals of an
isosceles trapezoid
are congruent.
Why??*Bonus*
proof due Monday
Ex: Find the value of
x if AC = 2x + 10
and BD = 3x + 4
A
D
B
C
Kites
Kites
Theorem 6-17:
Recap: What are the The diagonals of a kite
requirements in
are
order to be a kite?
_____________.
What other quadrilaterals share
this characteristic?
*note*: one pair of opp. <‘s is bisected (the
diag. that splits the congruent legs)
Example:
Find the measures of
the numbered
angles.
Find the measures
of the numbered
angles.
32˚
46˚
What rules can we derive for kites?
1.) diagonals are perpendicular
2.)adjacent sides congruent,
but not all sides congruent