ADVANCED GEOMETRY
5.4/5 Four Sided Polygons / Properties of Quadrilaterals
Learner Objective: I can solve problems using properties of special quadrilaterals.
What is a polygon?
Characteristics of a Polygon:
 _________ figure
 Consists only of ___________
 Consecutive sides ____________ only at
____________.
 Non-Consecutive sides do not _______________.
 Each __________ belongs to exactly _______ sides.
Are these Polygons? Why or why not?
A Convex Polygon is a polygon in which each
_____________ angle has a measure
________ ________ 180°.
Example
A Concave Polygon is a polygon in which at
least _________ ___________ angle has a
measure ___________ ___________ 180°.
Example
A Diagonal of a Polygon is any _____________ that connects two ____________________
(nonadjacent) vertices of the polygon.
Draw all of the diagonals of this polygon.
How many are there?
A Quadrilateral is a _________ sided polygon.
SPECIAL QUADRILATERALS:
A Parallelogram is a _______________ in which _________ __________ of opposite sides
are ____________.
Properties of Parallelograms:
1. Opposite sides are ____________.
2. Opposite angles are _____________.
3. Diagonals ____________ each other.
4. Any pair of consecutive angles are _____________.
A Rectangle is a _______________ in which _____ _________ _________ angle is a
_________ angle.
Properties of Rectangles:
1. All properties of a ______________ apply (by
definition)
a. Opposite sides are ____________
b. Opposite sides are ______________
c. Opposite angles are _____________
d. Diagonals ___________ each other.
e. Any pair of consecutive angles are
____________.
2. All angles are ____________ angles.
3. The diagonals are ______________.
A Rhombus is a _______________ in which ____ ___________ ________ consecutive
sides are ______________.
Properties of a Rhombus:
1. All properties of a ______________ apply (by
definition)
a. Opposite sides are ____________
b. Opposite sides are ______________
c. Opposite angles are _____________
d. Diagonals ___________ each other.
e. Any pair of consecutive angles are
____________.
2. All sides are ____________.
3. Diagonals are _______________
_______________ of each other
4. Diagonals _____________ the angles
5. Diagonals __________ the rhombus into ______
________ _________ triangles.
A Square is a _______________ that is both a ______________ and a ______________.
Properties of a Square:
1. All properties of a ___________ apply (by
definition)
a. Opposite sides are ____________
b. Opposite sides are ______________
c. Opposite angles are _____________
d. Diagonals ___________ each other.
e. Any pair of consecutive angles are
____________.
2. All properties of a ______________ apply (by
definition)
a. All angles are _________ angles.
b. The diagonals are ___________.
3. All properties of a ____________ apply (by
definition)
a. All sides are ____________.
b. Diagonals are _____________
____________ of each other
c. Diagonals ___________ the angles.
4. The diagonals form _______ _____________
________ _________ triangles (45°-45°-90°).
A Kite is a ________________ in which two ____________ pairs of ______________ sides
are _______________.
Properties of a Kite:
1. Diagonals are ________________
Half Properties
2. One Diagonal is the ______________
______________ of the other.
3. One Diagonal ____________ a pair of
______________ angles.
4. One pair of opposite angles are congruent
A Trapezoid is a _______________ with ___________ one pair of ____________ sides.
The parallel sides are called __________ of the trapezoid.
Properties of a Trapezoid:
One pair of opposite sides parallel (by Definition)
An Isosceles Trapezoid is a trapezoid in which the _________________ sides (legs) are
_____________.
Properties of an Isosceles Trapezoid:
1. Leg are __________ (by definition)
2. Bases are __________ (by definition)
3. Lower base angles are ______________
4. Upper base angles are ______________
5. Diagonals are _____________
6. Any lower base angle is _________________ to
any upper base angle
Complete this Venn Diagram using the words in the column below.
Trapezoid
Parallelogram
Rhombus
Square
Rectangle
Quadrilateral
Isosceles Trapezoid
Where would “Kites”
be if we wanted to
include them in this
diagram?
Fill in the blank with one of these – Some, All, or No.
_______ trapezoids are parallelograms
_______ rhombuses are squares
_______ rectangles are rhombuses
_______ squares are rhombuses
_______ squares are rectangles
_______ rhombuses are kites
_______ parallelograms are quadrilaterals
_______ trapezoids are rectangles
_______ isosceles trapezoids are parallelograms
_______ rectangles are parallelograms
_______ kites are rhombuses