Chapter 5 “In a Nutshell”
The “Quadrilateral Family Tree” is shown below. Next to each appropriate number, please fill in the name and properties of each shape.
Quadrilateral
1. ________________________

A 4-sided polygon
____________________________
(D)
1
Parallelogram
3. ________________________
3
2
7

A quadrilateral with 2 sets of parallel sides
___________________________________________________________
(D)

If a quadrilateral is a parallelogram, opposite sides are congruent. (T)
___________________________________________________________

If a quadrilateral is a parallelogram, opposite angles are congruent.(T)
___________________________________________________________

If a quadrilateral is a parallelogram, diagonals bisect each other. (T)
___________________________________________________________

If a quadrilateral is a parallelogram, one pair of opposite sides are congruent and parallel
(T)
8
4
5
6
4. ________________________
Rectangle
Always keep this family tree
in mind when thinking
about the properties
individual quadrilaterals.

___________________________________________________________
(D)
A quadrilateral with four 90o angles.

___________________________________________________________
(T)
In a rectangle, diagonals are congruent.

In a rectangle, BOTH diagonals create FOUR isosceles triangles

If a parallelogram has ONE right angle, then it is a rectangle (T)
Rhombus
5. ________________________
1
3
2

A quadrilateral with 4 congruent sides.
____________________________________________________________
(D)

In a rhombus, each diagonal bisects 2 angles.
____________________________________________________________
(T)

In a rhombus, diagonals are perpendicular.
____________________________________________________________
(T)
7
8
4
5
6. ________________________
Square

A quadrilateral with 4 congruent sides and at least one 90o angle.
____________________________________________________________
(D)
Trapezoid
7. ________________________
6

A quadrilateral with exactly one set of parallel sides.
___________________________________________________________
(D)

The median of a trapezoid is parallel to the base and measures the
average of the bases.
___________________________________________________________
(T)
Isosceles Trapezoid
8. ________________________

A trapezoid with congruent legs.
___________________________________________________________ (D)

Diagonals of an isosceles trapezoid are congruent.
___________________________________________________________


Base angles of a isosceles trapezoid are congruent.
(T)
Ways to prove that a quadrilateral is a ….
Parallelogram
Definition
Theorem
Theorem
Rectangle
If a parallelogram has at least one 90o angle,
 __________________________________________
then the parallelogram is a rectangle.
__________________________________________ (T)
Rhombus
If a parallelogram has 2 consecutive congruent
 __________________________________________
side, then the parallelogram is a rhombus.
__________________________________________ (T)
Theorem
Theorem
Some Trapezoid Terminology
One of the parallel sides of a trapezoid. (D)
Base: ________________________________________
A
The non-parallel sides of a trapezoid.
(D)
Legs: ________________________________________
B
The angles included between a base and the two legs
Base Angles: __________________________________
of a trapezoid. (D, 2 sets)
__________________________________
The segment whose endpoints are the
Median: _____________________________________
C
D
midpoints of the legs of a trapezoid. (D)
_____________________________________
Other “Miscellaneous Theorems”

T: If three (or more) parallel lines cut off congruent segments
on one transversal, they cut off congruent segments on
EVERY transversal.

T: If a line contains the midpoint of one side of a triangle and
is parallel to another side of the triangle, then it passes through
the midpoint of the 3rd side of the triangle.

T: If a segment joins the midpoints of two sides of a triangle,
then this segment and is parallel to the 3rd side of the triangle
and measures half the length of the 3rd side.

The midpoint of the hypotenuse of a right triangle is
equidistant from the three vertices.
½b
b