Unit 5

NAME ____________________________
GEOMETRY
UNIT 5 Quadrilateral Families
Date Page(s) Topic Homework
11/26 3 Quadrilateral Family Talk True/False Worksheet
11/27 4 Properties of a Parallelogram Fill in every missing angle
and side on the
Parallelogram on Pg. 4a
11/28 5 Apply properties of parallelograms Pg. 324 # 1,5,7-9,16,32
11/29 6 Properties of a Rectangle Fill in every missing angle
and side on the rectangle
on Pg. 6a
11/30 7 Apply properties of a rectangle Pg. 334 #44,51,67-69
12/3 8 QUIZ
Properties of a Rhombus
Fill in every missing angle
and side on the Rhombus
on Pg. 8a
12/4 9 Apply properties of a Rhombus Pg. 334 #1,9,64-66
12/5 10,11 Properties of a Square, Apply
properties
Pg. 334 #25-34,45, fill in
missing sides and angles for
square
12/6 Review all properties
QUIZ
Classifying Quadrilaterals
Worksheet
12/7 12,13 Properties of a Trapezoid and a Kite Fill in every missing angle
and side on the isosceles
trapezoid on Pg. 12a
12/10 13,14 Apply properties of a trapezoid and Worksheet- G.G.40
others
12/11 Review Ticket In
12/12 TEST None
1

PARALLELOGRAMS
Properties
All of the properties of a Quadrilateral
Plus 5 of it’s own:
1 1
2 2
3
4
5
Ways to prove
1.)
Ways to prove a parallelogram
2.)
3.)
4.)
5.)
1.) If the following is a parallelogram, solve for x 2.)If the following is a parallelogram, solve for x &y
50
4x-35
2x-4
x+4
y
2x+15
4

Decide whether or not the following are parallelograms and JUSTIFY your answer.
3.) 4.) 5.)
6.) 7.) 8.)
9.) Prove Quadrilateral ABCD is NOT a parallelogram, Justify your answer
A
117
B
C
41
D
10.) Determine the truth value of the following:
a.) A parallelogram has diagonals that bisect each other and the diagonals are congruent
b.) If a quadrilateral does not have 4 sides then a parallelogram has both sets of opposite sides parallel.
c.) A parallelogram has all sides congruent if and only if parallelograms diagonals are perpendicular
d.) A parallelogram doesn’t have both sets of opposite angles congruent or consecutive angles are
supplementary in a parallelogram.
5

RECTANGLE
Properties
All of the properties of a PARALLELOGRAM:
Plus 2 of it’s own:
1 There are 4 sides 1
2 The sum of the angles is 360 2
3 Both pairs of opposite sides are
4 Both pairs of opposite sides are
5 Diagonals
6 Consecutive angles are
7 Opposite angles are
1.)
Ways to prove a Rectangle
2.)
3.)
–
2.)
D
3 1
4
2
Z
-
J
Y
J
6

3.) Prove that the following is a rectangle, justify your answer.
58
8
32
4.) Which reason could be used to prove that a parallelogram is a rectangle?
1) Diagonals are congruent.
2) Opposite sides are parallel.
3) Diagonals are perpendicular.
4) Opposite angles are congruent
5.) Label ALL angles and line segments if RIGH is a Rectangle
I
R
48
G
H
7

RHOMBUS
Properties
All of the properties of a PARALLELOGRAM:
1 There are 4 sides 1
Plus 3 of it’s own:
2 The sum of the angles is 360 2
3 Both pairs of opposite sides are 3
4 Both pairs of opposite sides are
5 Diagonals
6 Consecutive angles are
7 Opposite angles are
1.)
Ways to prove a Rhombus
2.)
3.)
1.) In the diagram below of rhombus ABCD, m∠C = 100. What is m∠DBC?
8

2.) Fill in ALL angles and line segments for the rhombus
18
3.) Prove that ABDE is a rhombus; If ABE is an isosceles triangle with vertex A. Justify your answer
A
88
46
46
B
E
88
D
9

SQUARE
Properties
All of the properties of a Plus the extras from a RECTANGLE
PARALLELOGRAM
1 There are 4 sides 1 1
Plus the extras from a RHOMBUS
2 The sum of the angles is 360 2 2
3 Both pairs of opposite sides are 3
4 Both pairs of opposite sides are
5 Diagonals
6 Consecutive angles are
7 Opposite angles are
Ways to prove (too many to write them all, so this is the concept)
1.)
Ways to prove a Square
2.)
1.) The diagonals of a quadrilateral are congruent but do not bisect each other. This quadrilateral is
1) an isosceles trapezoid
2) a parallelogram
3) a rectangle
4) a rhombus
10

-
A
B
C
ABCD is a
parallelogram with
AC=DB
2
1 3

TRAPEZOID
Properties
All of the properties of a Quadrilateral
1 1
Plus 2 of it’s own
2 2
Add on for
Isosceles Trapezoid
All of the properties of a TRAPEZOID
Plus 3 of it’s own
1 Sum of the angles is 360 1
2 4 sides 2
3 1 pair of opposite sides are parallel 3
4 1 pair of opposite sides are not parallel
Add on for
Right Trapezoid
All of the properties of a TRAPEZOID
1 Sum of the angles is 360 1
Plus 1 of it’s own
2 4 sides
3 1 pair of opposite sides are parallel
4 1 pair of opposite sides are not parallel
1.)
Ways to prove a Trapezoid
2.)
12

1.)
Ways to prove an Isosceles Trapezoid
2.)
1.)
Ways to prove a Right Trapezoid
KITE
Properties
The properties of a Quadrilateral
1 1
Plus 2 of it’s own
2 2
1.) Fill in ALL the missing measurements
30
3
20
2.) In the diagram below of isosceles trapezoid DEFG, DE || GF, DE = 4x − 2, EF = 3x + 2, FG = 5x − 3,
and GD = 2x + 5. Find the value of x.
13

3.) In the diagram below, LATE is an isosceles trapezoid with LE ≅ AT , LA = 24, ET = 40, and
AT = 10. Altitudes LF and AG are drawn. What is the length of LF?
4.)Find the measure of