Transcript Trapezoids

Trapezoids
Trapezoid - A quadrilateral with exactly
one pair of parallel sides.
Bases - The parallel sides of a trapezoid.
Legs - The nonparallel sides of a
trapezoid.
Base angles - The angles formed by a
base and one of the legs.
Trapezoids
Isosceles trapezoid - A trapezoid with
congruent legs.
Theorem 8.18
• Both pairs of base angles of an isosceles
trapezoid are congruent.
Theorem 8.19
• The diagonals of an isosceles trapezoid are
congruent.
The sides of a picture frame appear to be two adjacent
trapezoids. Determine if they are isosceles trapezoids.
Answer: yes
QRST is a quadrilateral with vertices Q(–3, –2), R(–2, 2),
S(1, 4), and T(6, 4).
a. Verify that QRST is a trapezoid.
Answer: Exactly one pair of opposite sides is parallel.
Therefore, QRST is a trapezoid.
b. Determine whether QRST is an isosceles trapezoid.
Explain.
Answer: Since the legs are not congruent, QRST
is not an isosceles trapezoid.
Trapezoids
Median of a trapezoid - A segment that joins
the midpoints of the legs of the trapezoid.
Theorem 8.20
• The median of a trapezoid is parallel to the
bases and has a length equal to half the sum
of the lengths of the bases.
WXYZ is an isosceles trapezoid
with median
a.
Answer:
b.
Answer:
Because