Plane Geometry
Chapter 6 Review
Name: ____________________________
Things To Know…
a) properties of all the shapes
b) midsegment formula
c) diagonal formula
d) interior/exterior angle formulas
e) polygon names
f) quadrilateral reasoning
Practice Problems:
1. How many diagonals does a 14-gon have?
2. How many diagonals does a 23-gon have?
3. Find mA.
4. Find the value of x.
A
88
86
D
87
B
85
71
120
(10x – 6)
C
5. Is there enough information to say these are parallelograms? Explain why or why not.
a.
b.
60
60
c.
d.
42
138
7
42
7
6. PQRS is a parallelogram. Find each of the following:
PQ = ____________
P
QR = ____________
8
mPQR = _____________
39
S
mR = _____________
Q
110
R
10
mPSR = _____________
mSQR = _____________
7. CDEF is a parallelogram. Find the values of x and y.
C
5x
x = _______________
D
y = _______________
18
3y + 6
125
E
F
8. JKLM is a rectangle. Find each of the following:
ML = _______________
12
J
7.5
JM = _______________
N
JN = _______________
MK = ______________
mJML = ______________
mKML = ______________
mMJL = ______________
K
9
62
M
L
9. ABCD is a rhombus. Find each of the following:
A
AD = _____________
B
7
x = ______________
E
mAEB = ________________
ED = _____________
D
7x – 9
28
C
5
mADB = ______________
mABC= ______________
mACD = ______________
mBAD = ______________
EC=_________________
E
F
10. EFGH is a square. Find each of the following:
FH = ______________
I
8x – 1
4
mEFG = _____________
mEIH = _____________
H
10x – 9
G
EI = ______________
EF = _____________
mEFH = ______________
mGEH = ______________
11. Solve for x:
12. Solve for x:
14
x
x
6
15
11
13. Solve for x:
14. Find all missing angles:
115
x
120
15. Find x.
2x
16
6x
16. Answer each of the following as sometimes, always, or never.
a) A rhombus is ________________________ a parallelogram.
b) A trapezoid is ________________________ a parallelogram.
c) A parallelogram is _______________________ a square.
d) A square is _________________________ a rhombus.
17. What is the most specific name for each quadrilateral:
a) A quadrilateral with diagonals that are congruent and bisect each other.
b) A parallelogram with at least 1 right angle.
c) A parallelogram with all sides congruent.
18. List each quadrilateral for which the statement is true.
parallelogram
rhombus
rectangle
square
a. Opposite sides are congruent.
b. Diagonals bisect each other.
c. It has four congruent sides and four right angles.
d. It has four right angles.
e. Diagonals are perpendicular.
f. The diagonals are congruent.
19a) Find the sum of the interior angles of a decagon.
b) Find the measure of each interior angle of a 13-gon.
20a) Find the sum of the exterior angles of a 35-gon.
b) Find the number of sides of a polygon whose exterior angles measure
60 each.