WS Polygons and Quadrilaterals
Name: __________________________
POLYGONS
1.) Given below is the number of sides of a polygon. Give the name of the polygon.
Ten ____________________
Nine____________________
Twelve____________________
Five____________________
Twenty____________________
Thirteen____________________
Seven____________________
Eight____________________
2.) Use the polygon to the right to answer the questions.
Name the polygon according to the number of sides. _________________________
Is the polygon concave or convex? ____________________
Is the polygon regular? Explain. __________________________________________
Name one side of the polygon. _____________________
Name one angle of the polygon. ____________________
Name all vertices of the polygon. ________________________________
3.) Find the sum of the interior angles, each interior angle, and each exterior angle of the following
regular polygons.
Polygon
Octagon
Hexagon
14-gon
Nonagon
Dodecagon
Quadrilateral
Sum of interior angles
Each interior angle
Each exterior angle
WS Polygons and Quadrilaterals
Name: __________________________
4.) The measure of one exterior angle of a regular polygon is given. Find the number of sides.
120 degrees ______________________
60 degrees _____________________
5.) Find the missing values.
Find the m ∠A. __________
Find the m ∠ 1. __________
Find the value of “x”.
6.)
7.)
8.)
9.)
Solve for the following quadrilateral. (not a Parallelogram!)
10.)
L
6x - 7
12x M
x = _________
m<NOL = ___________
O
4x - 1
7x + 3 N
WS Polygons and Quadrilaterals
Name: __________________________
WS Polygons and Quadrilaterals
Name: __________________________
PARALLELOGRAMS
Given KLMN is a parallelogram, find the following:
11.) KN = 3x – 5
12.) KL =
x
2
LM = x + 9
KN = _______
MN = 2x - 9
KL = _______
13.) m <K = 4x + 11
m <L = 6x – 1
m <M = _______
14.) m <K = 31
m <M = 2x – 1
m <L = _______
15.) KL = 2x
16.) m <L = x – 40
3
x
4
MN = 3y + 4
m <N =
LM = x + 7
KN = 2y
KL = _______
LM = _______
m <L = _______
Find each value of x and y, for which each is a parallelogram.
17.)
18.)
x = _______
x = ________
19.)
x =_________
y = _________
Is ABCD a parallelogram?
20.) A (0, 0)
B (5, 0)
C (5, 4)
D (0, 4)
yes / no
21.) A (0, 0)
B (-4, 0)
C (-6, 3)
D (-1, 3)
yes / no
WS Polygons and Quadrilaterals
Name: __________________________
Determine the values of x and y for which ABCD is a parallelogram.
22.) AB = 2x + 4
CD = 4x – 20
AD = 2y
BC = y + 5
x= _____ y = _____
23.) m <A = 2x – 60
m <D = x – 5
AB = 4y + 6
CD = 6y – 10
x= _____ y = _____
24.) AB = 6x + 30
BC = 2x – 5
CD = 2y – 10
AD = y – 35
x= _____ y = _____
Find the value of each variable in the parallelogram.
25.)
26.)
27.)
28.)
For what value of x is the quadrilateral a parallelogram?
29.)
30.)
Classify the special quadrilateral. Then find the values of x and y.
31.)
32.)
Give the most specific name for the quadrilateral.
33.)
34.)
35.)
WS Polygons and Quadrilaterals
Name: __________________________
Find m ∠ B.
36.)
37.)
Find the length of the midsegment of the trapezoid.
38.)
39.)
Determine whether each of the following statements is always, sometimes, or never true. You may
abbreviate with an A, S, or N.
40. __________Opposite angles of an isosceles trapezoid are supplementary.
41. __________ Rectangles are squares.
42. __________The diagonals of a parallelogram are congruent.
43. __________ Rhombi are squares.
44. __________The midpoints of the legs of a trapezoid are the endpoints of the median.
45. __________Squares are rhombi.
46. __________The diagonal of a parallelogram separates it into two congruent triangles.
47. __________Consecutive angles of a parallelogram are complementary.
48. __________An equiangular quadrilateral is a square.
49. __________Opposite angles of a parallelogram are congruent.
50. __________A parallelogram is a quadrilateral.
51. __________Consecutive sides of a parallelogram are congruent.
52. __________A rectangle is a rhombus.
53. __________The diagonals of a rectangle are congruent.
54. __________A trapezoid has a right angle.
55. __________One leg of a trapezoid is congruent to both bases.
56. __________The diagonals of a rhombus are perpendicular.
57. __________An equilateral polygon is regular.
58. __________The median of a trapezoid is parallel to both bases.
59. __________A square is a parallelogram.