Download Final Exam Review Ch. 5

FINAL EXAM REVIEW
Chapter 5
Key Concepts
Chapter 5 Vocabulary
parallelogram
► opposite sides
► opposite angles
► diagonals
rectangle
rhombus
square
trapezoid
Defn. of a Parallelogram
A quadrilateral with both pairs of
opposite sides parallel
A
B
In
D
C
ABCD,
AB
DC and
AD
BC
Theorem
Opposite sides of a parallelogram are
congruent.
Theorem
Opposite angles of a parallelogram are
congruent.
Theorem
Diagonals of a parallelogram bisect each
other.
Theorem
One pair of opp. sides both // and ~=
Parallelogram
The Five Ways to Show a
Quadrilateral is a Parallelogram
1) Defn. of
2) Both pairs of opp. sides =~
3) One pair of opp. sides both // and ~=
7
4) Both pairs of opp.
~
‘s =
5) Diagonals bisect each other
Theorem
If 2 lines are parallel, then all points on one line
are equidistant from the other line.
A
B
l
m
C
D
AC = BD
Theorem
If 3 parallel lines cut off congruent segments on
one transversal, then they cut off congruent
segments on every transversal.
A
B
C
If
X
AB = BC
then XY = YZ
Y
Z
Theorem
A line that contains the midpoint of one side of
a triangle and is parallel to another side passes
through the midpoint of the third side.
X
M
Y
If M is the midpoint of XY
then N is the midpoint of XZ
N
Z
Theorem
A segment that joins the midpoints of 2 sides
of a triangle;
1. is parallel to the third side.
2. is half as long as the third side.
X
M
Y
1.MN
YZ
2.MN = ½YZ
N
Z
Theorem: The diagonals of a
rectangle are congruent
Theorem: The diagonals of a
rhombus are perpendicular.
Theorem: Each diagonal of a rhombus
bisects two angles of the rhombus.
Theorem: The midpoint of the
hypotenuse of a right triangle is
equidistant from all three vertices.
.
Theorem: If an angle of a parallelogram is a right
angle, then the parallelogram is a rectangle.
Theorem: If two consecutive sides of a
parallelogram are congruent, then the
parallelogram is a rhombus.
Trapezoid (Defn.)
A quadrilateral with exactly one pair of
parallel sides.
leg
base
base
leg
IsoscelesTrapezoid (Defn.)
A trapezoid with congruent legs.
Theorem
Base angles of an isosceles trapezoid
are congruent.
Theorem
The median of a trapezoid:
1. is parallel to the bases.
2. has a length equal to the average of the
base lengths.
A
XY = ½(AB + CD)
X
C
B
median
Y
D
Homework
► Chapter
5 Review WS