Download Name Date ______ Geometry Period ______ Definitions: Polygons

Name _____________________________
Geometry
Date _____________
Period _____________
Definitions:
Polygons: a ____________________________
straight-sided figure with
____________________________.
Quadrilaterals: a polygon with ____________________________ and
____________________________.
Note: The sum of _______________ the angles of a quadrilateral is ________________
Ex: What is the missing angle?
70º
70º
?
110º
Parallelograms: a quadrilateral where ________________________ are ________________
Properties of a Parallelogram
1)
2)
3)
4)
5)
1
Name _____________________________
Geometry
Mark the following on the picture of the parallelogram below:
Date _____________
Period _____________
Congruent angles
Congruent sides
Parallel sides
Supplementary angles
Diagonals
If quadrilateral FRAC is a parallelogram, what congruence statements can you make?
R
F
C
A
Ex #1) MATH is a parallelogram. Find the values of w, x, y, and z.
M
wo
yo
o
H 55
A
zo
T
Ex #2) DUCK is a parallelogram. Find the values of w, x, y, and z.
D
yo
113o
o
C z
U
wo
K
Directions: Determine whether each of the following figures are parallelograms.
Example #1)
Example #2)
15
F
6
C
J
R
80°
K
7
16
A
100°
100°
A
P
2
Name _____________________________
Geometry
Example #3)
Example #4)
E
70°
120°
120°
M
V
Date _____________
Period _____________
105°
102°
A
N
A
78°
R
K
Directions: Find the value of w, x, y, and z assuming each figure is a parallelogram.
Example #1)
Example #2)
y
x
105°
31°
y°
78°
z
44°
x°
29 °
Example #3)
z°
Example #4)
15
z°
73°
w°
x°
y°
z°
55°
y°
x
Example #5) Given parallelogram XCVB with <X=10x-9, and <C=5x+9. Find <V and <B.
Example #6) In parallelogram ABCD AB = 2x + 5, CD = y + 1, AD = y + 5, and BC = 3x – 4. Find the
measures of the sides.
3
Name _____________________________
Geometry
Date _____________
Period _____________
Rectangle Properties:
1)
2)
3)
4
Name _____________________________
Date _____________
Geometry
Period _____________
Name two properties that hold for all rectangles but not necessarily for all parallelograms.
1)
2)
Discussion:
Can it be proved that a rectangle is a parallelogram?
If so how?
Use rectangle ABCD and the given information to solve each problem.
#1) BC=12, find AD
A
#2) DB=18, find DE
1
B
2
3
E
4
D
#3) <1=80°, find <4
C
Directions: Find the values of x and y assuming RSTV is a rectangle.
Example #1)
VW=2x+y
WS=36
RS=x-y
VT=9
Example #2)
VR=y
TS=x+11
VT=y-3x
RS=x+2
S
T
S
T
W
W
V
V
R
R
Directions: If ABCD is a rectangle, find the value of x.
Example #1)
Example #2)
AC=x2
DB=6x-8
Angle DAC=4x+8
Angle CAB=5x-8
C
D
C
D
E
E
5
A
B
A
B
Name _____________________________
Geometry
Date _____________
Period _____________
Properties of Rhombi
1)
2)
3)
Example #1) Use rhombus PQRS and the given information to solve each problem.
a. ST = 13, find SQ
Q
b. m< PRS = 17, find m<QRS
P
R
c. Find m<STR
d. If SP = 4x – 3 and PQ = 18 + x, find x
S
Example #2) Determine whether the following statements are true or false using the diagram of rhombus RSTV
with SV=42.
S
A) RT=42
T
P
B) PS=21
R
V
C) RT perpendicular to SV
6
Name _____________________________
Date _____________
Geometry
Period _____________
Example #3) Use Rhombus BCDE and the given information to solve each problem
a) If m<EBC = 132.6, find m<EBD
C
b) If m<BDC = 25.9, find m<EDC
c) If m< BEC = 2x + 10 and m<CED =
5x – 20, find x
B
D
E
2
d) If m< CBD = 2x + 24, and m< EBD = x , find x.
Properties of a Square:
1)
7
Name _____________________________
Geometry
Date _____________
Period _____________
Parallelograms
Parallelogram
Rectangle
Rhombus
Square
opposite sides parallel
opposite sides congruent
opposite angles congruent
consecutive angles supplementary
four right angles
four congruent sides
diagonals bisect each other
diagonals congruent
diagonals perpendicular
diagonals angle bisector
Properties of Trapezoids
1)
2)
Isosceles Trapezoid: A trapezoid where the __________________________________.
Properties of Isosceles Trapezoids
1)
2)
Directions: Label the following on a picture of a trapezoid
Base
Legs
Base angles
median
8
Name _____________________________
Geometry
Directions: Draw a trapezoid with each set of characteristics.
A) both bases are shorter than the legs.
Date _____________
Period _____________
B) Contains a right angle.
C) Has two obtuse angles.
Directions: ABCD is an isosceles trapezoid with bases AD and BC. Use the figure and the given information
to solve each problem.
A) If BA=9, find CD.
B
B) If AC=4y-5 and BD=2y+3, find AC and BD.
A
C
D
C) If Angle BAD=123, find Angle CBA.
Example #2) Given trapezoid GHIJ with median KL, find the value of x.
G
K
J
3x-1
10
7x+1
H
L
I
Example #3) Given trapezoid RSTV with median MN, find the value of x.
6x – 3
15
8x + 5
9
Name _____________________________
Date _____________
Geometry
Period _____________
Example #3) HJKL is an isosceles trapezoid with bases HJ and LK. If LK = 30 and HJ = 42 find RS.
30
L
K
R
S
H
J
42
Example #4) HJKL is an isosceles trapezoid with bases HJ and LK. If RS = 17 and HJ = 14 find LK.
L
K
17
R
S
H
J
14
Example #5)
HJKL is an isosceles trapezoid with bases HJ and LK. If RS = x + 5 and HJ + LK = 4x + 6 find RS.
L
K
x+5
R
S
J
H
Example #6) HJKL is an isosceles trapezoid with bases HJ and LK. If m<LRS = 66, find m<KSR.
L
K
66
R
S
H
J
10
Name _____________________________
Geometry
Date _____________
Period _____________
Looking at the chart, answer the following questions:
a) Are all rectangles quadrilaterals?
b) Are all parallelograms rectangles?
c) Are all rectangles squares?
d) Are all squares rectangles?
e) Are all squares parallelograms?
Directions: Make a Venn Diagram of all the Quadrilaterals to show how they are related to each other.
How do I tell if it’s a
Parallelogram?

Use the slope formula to find the slope of opposite pairs of sides.

If the slope of opposite pairs of sides is the same then it is a parallelogram.
How do I tell if it’s a
Rectangle?

Check for a parallelogram and then follow the steps below.

Look at the slope of two consecutive (next to) sides.

If the slope is the –reciprocal then it is a rectangle.
How do I tell if it’s a

Rhombus?
Check for a parallelogram and then follow the steps below.
11
Name _____________________________
Date _____________
Geometry
Period _____________
 Use the distance formula to find the distance of two consecutive sides.

If the distance of two consecutive sides is the same then it is a rhombus.
How do I tell if it’s a
Square?

Check for a parallelogram, rhombus and rectangle.

Needs to meet all three requirements to be a square.
Example #1)
A(0,1)
B(2,0)
C(3,2)
D(1,3)
12
Name _____________________________
Geometry
Example #2)
A(-1,0)
B(1,0)
C(3,5)
D(1,5)
Date _____________
Period _____________
Example #3)
A(8,11)
B(2,3)
C(3,7)
D(9,15)
13