Download Geometry Section 6.6 Notes 4/8/13 - 4/9/13

BellWork
OUTCOMES
You will be able to:
identify trapezoids by their properties.
 solve for missing information using trapezoid properties.
Identify kites by their properties.
Solve for missing information using kite properties.
Section 6.5 – Trapezoids and Kites
exactly one pair of parallel sides
A trapezoid is a quadrilateral with _______________________.
bases
The parallel sides are called the __________.
legs
The nonparallel sides are called the _________.
base
leg
leg
base
Base Angles
Theorem 6.14: If a trapezoid is isosceles,
congruent
then each pair of base angles is ___________.
A
∠A ≅ ∠B, ∠C ≅ ∠D
D
B
**Isosceles: two
congruent side.**
C
Theorem 6.15: If a trapezoid has a pair of congruent
base angles, then it is an ______________________.
Isosceles Trapezoid
A
B
If ∠C ≅ ∠D, then
ABCD is an isosceles
Trapezoid.
D
C
Theorem 6.16: A trapezoid is isosceles if and only if its
congruent
diagonals are ________________.
A
B
ABCD is an isosceles
trapezoid
if and only if AC ≅ BD.
D
C
Examples
• Find the angle measures of ABCD.
J
M
K
L
Midsegment of a Trapezoid
Midsegment of a Trapezoid: the segment that
connects the midpoint of its legs.
Theorem 6.17
MP = ½ (NO + LQ)
Kites and their Properties
• Kite: A quadrilateral that has two pairs of
consecutive congruent sides, but opposite
sides are not congruent.
Theorems about Kites
Pythagorean Theorem
• Reminder: Solve the sides of right triangles
with the Pythagorean Theorem.
• a2 + b2 = c2
• The hypotenuse is always the longest side,
across from the right angle.
c
a
b
Examples
Examples
Always, Sometimes, or Never???
never
always
sometimes
always
always
Exit Ticket
Example 5. Decide whether the following statements are
always, sometimes, or never true.
Sometimes
(a) Diagonals of a trapezoid are congruent. _____________
Always
(b) Opposite sides of a rectangle are congruent. __________
Always
(c) A square is a rectangle. _________
Sometimes
(d) All angles of a parallelogram are congruent. ______________
(e) Opposite angles of an isosceles trapezoid are congruent. __________
Never
Sometimes
(f) The diagonals of a parallelogram are perpendicular. ______________