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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
A trapezoid is a quadrilateral with _______________________.
The parallel sides are called the __________.
The nonparallel sides are called the _________.
exactly one pair of parallel sides
bases
legs
base
base
leg leg
Base Angles
Theorem 6.14: If a trapezoid is isosceles, then each pair of base angles is ___________.congruent
A
D
B
C
∠A ≅ ∠B, ∠C ≅ ∠D**Isosceles: two congruent side.**
Theorem 6.15: If a trapezoid has a pair of congruent base angles, then it is an ______________________.Isosceles Trapezoid
A
D
B
C
If ∠C ≅ ∠D, thenABCD is an isoscelesTrapezoid.
Theorem 6.16: A trapezoid is isosceles if and only if its diagonals are ________________.congruent
A
D
B
C
ABCD is an isoscelestrapezoidif and only if AC ≅ BD.
Examples
• Find the angle measures of ABCD.
L
J
M
K
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.
a
b
c
Examples
Examples
Always, Sometimes, or Never???
never
sometimes
always
always
always
Example 5. Decide whether the following statements are always, sometimes, or never true. (a) Diagonals of a trapezoid are congruent. _____________ (b) Opposite sides of a rectangle are congruent. __________ (c) A square is a rectangle. _________ (d) All angles of a parallelogram are congruent. ______________ (e) Opposite angles of an isosceles trapezoid are congruent. __________ (f) The diagonals of a parallelogram are perpendicular. ______________
Sometimes
Always
Always
Sometimes
Never
Sometimes
Exit Ticket