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Geometry B
Unit 5 – Polygons & Quadrilaterals
Review (Part I)
Name
Lesson 1
1) Determine if the figures are polygons. If it is, name it by the number of sides. If not, explain why it is
not, using the definition of a polygon. Use complete sentences.
2) Determine if the figures are regular or irregular. Also, determine if they are concave or convex. Explain
your answer for each with complete sentences
Lesson 4
3) Determine if the figures have line symmetry. If so, draw ALL lines of symmetry.
4) Determine if the figures have rotational symmetry. If so, give the angle of rotation and the order of
rotational symmetry.
Lesson 2-3 – Be sure to show work or explain your reasoning.
5) Why is the formula for the sum of the interior angles of a convex n-gon n  2  180 ?
6) Find the sum of the interior angles of convex dodecagon.
7) Draw a regular heptagon with a side length of 1.5 cm.
8) What is the sum of the exterior angles of a convex 65-gon?
9) Find the measure of each exterior angle of a regular nonagon.
10) Find the measure of each interior angle of
hexagon ABCDEF.
11) Find the measure of each exterior angle in
pentagon PQRST.
12) Find the area of the decagon, rounded to the nearest tenth.
Lesson 5/6 – Properties of Parallelograms, Rectangles, Rhombuses, and Squares
13) ABCD is a parallelogram. Find the following and explain your reasoning.
mABC  79 ; BC  62.4 , BD  75
a. BE =
b. AD =
c.
mCDA =
d. mDAB =
14)
In rectangle ABCD, find the following and explain your reasoning.
CD = 18, CE  19.8 , mADB  27
a. AB =
b.AE =
c. BD =
d. mABD =
;
e. AD =
15) WXYZ is a parallelogram. Find the following and explain your reasoning.
a. WX =
c. WZ =
b. mY =
16) In rhombus WXYZ, find the following and explain your reasoning.
WX  7a  1, WZ  9a  6 , YZ = 5a+8 , mXVY   8n  18  , mXYZ   5n  4 
a. WZ
X
b. The value of n
c. XZ
7a+1
W
e.
mXYV
Y
V
5a+8
9a-6
d. mXYZ
(5n+4)°
(8n+18)°
Z
17) Find the missing angles and distances for each diagram. You will have to use some trigonometry.
Rhombus ABCD
B
2 in
C
56°
2.5 in
F
E
I
1.8 in
A
D
J
Square FGHI
G
Parallelogram ABCD
B
C
75°
8
8
E
110°
25°110°
A
D
25°
Rectangle FGHI
F
4.3
G
I
J
10.6
H
H
Geometry B
Unit 5 – Polygons & Quadrilaterals
Review (Part II)
Name
Lesson 7/8/9 – Proving a Quadrilateral is a Parallelogram, Rectangle, Rhombus, or Square
Determine if each of the following is enough information to conclude that the quadrilateral is a
parallelogram, rectangle, rhombus, or square. Be sure to state the theorem.
All questions are quadrilateral EFRS with diagonals intersecting at point X.
18) FR  ES , EF  RS
Parallelogram:
Rectangle:
Rhombus:
Square:
19) EX  RX , FX  SX , ER  FS
Parallelogram:
Rectangle:
Rhombus:
Square:
20) EF
RS , FR ES , EF  ES
Parallelogram:
Rectangle:
Rhombus:
Square:
21) mEFR  70 , mSEF  110 , FR  ES
Parallelogram:
Rectangle:
Rhombus:
Square:
22) mFRS  90 , mSEF  90 , mESR  90 , ER  FS
Parallelogram:
Rectangle:
Rhombus:
Square:
23) Prove that the quadrilateral is a parallelogram using the given condition.
G(-2,5) R(3,6) A(-4,0) B(-9,-1)
a. Two pairs of parallel sides
b. 1 pair of sides are congruent and parallel
24) Prove that the quadrilateral is a rhombus by showing that it is a parallelogram with perpendicular
diagonals.
F(3,1) R(8,-4) E(7,-11) D(2,-6)
25) Prove that the quadrilateral is a rectangle by showing that it has four right angles.
F(-1,3) R(5,6) E(7,2) D(1,-1)
26) Determine if EFGH with given coordinates is a parallelogram, rectangle, rhombus, or square. You
must prove your answer and explain your reasoning.
E ( 3,0) , F ( 2,7) , G(5,8) , H (4,1)