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Geometry 8.5 Notes - Trapezoids
Name__________________________
Vocabulary
A trapezoid is a quadrilateral with ___________________________________________.

The parallel sides are the _______________.

For each of the bases of a trapezoid, there is a pair of
________________________, which are the two angles
that have that base as a side.

The nonparallel sides of a trapezoid are the ___________
of the trapezoid.
The trapezoid is an ____________ trapezoid if the legs of the
trapezoid are _________________.
Theorem 8.14: If a trapezoid is _______________________, then
each pair of base angles is
______________________________.
Theorem 8.15: If a trapezoid has a pair of congruent __________
________________, then it is an __________________________.
Theorem 8.16: A trapezoid is _________________ if and only if
_____________________________________________________.
The ____________ of a trapezoid is the segment that connects the
_____________________________________________________.
Theorem 8.17 _________________________________________:
The midsegment of a trapezoid is parallel to each base and its
length is one half the sum of the lengths of the bases.
Name __________________________________
Date ___________________
EXERCISES - TRAPEZOIDS
Points A, B, C, and D are the vertices of a quadrilateral. Determine whether ABCD
is a trapezoid.
1. A(–2, 3), B(3, 3), C(–1, –2), D(2, –2)
2. A(–3, 2), B(3, 0), C(4, 3), D(–2, 5)
3. A(–5, –3), B(–1, –1), C(–1, 3), D(–3, 2)
Find m  F, m  G, and m  H.
4.


Find the value of x.
8.

5.
9.
Find the length of the midsegment of
the trapezoid.
6.
7.
10.
Geometry 8.5 Notes – Kites
Name_________________________
A ______ is a quadrilateral that has two pairs of _______________
______________ sides, but opposite sides are ________________.
Theorem 8.18: If a quadrilateral is a ___________________, then
_____________________________________________________.
Theorem 8.19: If a quadrilateral is a ________, then ___________
one pair of opposite angles are ____________________________.
EXERCISES
JKLM is a kite. Find m  K.
1.

Use Theorem 8.18 and the
Pythagorean Theorem to find the side
lengths of the kite. Write the lengths
in simplest radical form.
3.
2.
4.
5.
Find the value of x.