Download Geometry B

Geometry B
Name
Unit 5 Test
Date
Block
60
ANSWERS
Directions: This test is written to cover Unit 5. Please answer each question to the best of your
ability. If multiple steps are required, it is expected that you will show those steps. If the
appropriate work is not shown, then points may be deducted.
1. Which of the figures below does NOT represent a polygon? Explain why. (2 points)
A.
B.
A – because the segments do not
meet at endpoints, there is overlap
C.
For questions 2 & 3, use the figures A, B, and C below.
A.
B.
C.
2. Explain why figure “A” a regular convex polygon. (2 points)
All sides and angles congruent; all diagonals drawn inside
3. Explain why figure “B” is an irregular concave polygon. (2 points)
Not all angles congruent; diagonals can be drawn on outside
4. Determine if the figures have line symmetry. If so, draw ALL lines of symmetry.
a. Oval
b. Parallelogram
(1 point each)
No line symmetry
5. Determine if the figures have rotational symmetry. If so, give the angle of rotational symmetry
and the order of rotational symmetry. (1 point each)
a. Square
b. Right Triangle
90°; 4
No rotational
symmetry
6. What is the sum of the measures the interior angles of a convex nonagon? Show work to
support your answer. (2 points)
(9  2)  180  1260
7. What is measure of each exterior angle of a regular 24-gon? Show work to support your
answer. (2 points)
360  24  15
8. What is the measure of each interior angle of a regular octagon? Show work to support your
answer. (2 points)
(8  2)  180  1080  8  135
9. Find the value of a in hexagon ABCDEF. Show work to support your answer. (2 points)
2a  5a  4a  5a  3a  5a  720
24a  720
a  30
a = 30
10. Find the value of a in the quadrilateral below. (2 points)
a  127  71  102  360
a  300  360
a  60
a = 60
11. Given parallelogram ABCD to the right, find the following and explain your reasoning. (1 point
each)
mABC  114 ; CD = 34, BD = 56
E
b. BE = 28; diagonals bisect each other
A
c. mBCD = 66°; consecutive angles are supplementary
d. mADC = 114°; opposite angles are congruent
C
B
a. AB = 34; opposite sides are congruent
D
12. In rectangle ABCD, find the following and explain your reasoning.
CD  20 , CE  22 , and mBDA  27 (1 point each)
a. AB = 20; opposite sides are congruent
b. AE = 22; diagonals bisect each other
c. BD = 44;diagonals are congruent
d. mABD = 63°; all angles are right angles, 90 – 27
13. In rhombus QRST, find the following and explain your reasoning.
mRPS  5a  15 , mPQR  2a  3
(1 point each)
R
8x+3
4x+15
a. QT = 27; all sides congruent
2x+9
Q
b. a = 15; diagonals perpendicular
P
c. TR = 30; diagonals bisect each other
T
d. mQTP = 57°;cons ∠‘s supp & diagonals bisect opposite angles
14. Fill in the blanks for each diagram. You may have to use some trigonometry. (1 point each blank)
a. Rhombus ABCD
b. Square FGHI
mAEB = 90°
mFGH = 90°
mDAC = 65°
mFGI = 45°
mABE = 25°
mIHF = 45°
AB = 4.0
(Round to the nearest tenth.)
Show work below.
1.7
cos 65 
AB
1.7
AB 
 4.022....
cos 65
FH = 14.0
(Round to the nearest tenth.)
Show work below.
9.92  9.92  FH 2
196.02  FH 2
14.0007...  FH
S
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 reason. All questions are
quadrilateral QUAD with diagonals intersecting at point X. (2 points each)
15. QUA  ADQ , UQD  UAD
PARALLELOGRAM – both pairs of opposite angles are congruent
16. QU  UA  AD  QD , QUA  90
SQUARE – it’s a rhombus (all four sides congruent), which also makes it a parallelogram; it’s
also a rectangle (a parallelogram with one right angle)
17. QX  10 , UX  10 , AX  10 , DX  10
RECTANGLE – it’s a parallelogram (because diagonals bisect each other) with diagonals
congruent
18. For each statement, write “A” if the statement is always true, “S” if the statement is sometimes
true, and “N” if the statement is never true. (½ point each)
a. A parallelogram is a quadrilateral. A
b. A quadrilateral is a square.
S
c. A rectangle is a square.
S
d. A square is a rectangle.
A
e. A parallelogram is a rhombus.
S
f. A rhombus is a parallelogram. A
For questions 19 – 22, circle one response. (1 point each)
19. Which of the following quadrilaterals have diagonals congruent?
a. parallelogram, rhombus, rectangle, square
b. rectangle, square, rhombus
c. rhombus, square,
d. rectangle, square
20. Which of the following quadrilaterals have perpendicular diagonals?
a. parallelogram, rhombus, rectangle, square
b. rhombus, square, rectangle
c. rectangle, square
d. rhombus, square
21. Which of the following quadrilaterals have diagonals bisect each other?
a. parallelogram, rhombus, rectangle, square
b. parallelogram, rhombus
c. parallelogram, rectangle
d. parallelogram, rhombus, square
22. Which of the following quadrilaterals have diagonals bisect the opposite angles?
a. parallelogram, rhombus, rectangle, square
b. rectangle, rhombus, square
c. rhombus, square
d. rectangle, square
23. Determine if quadrilateral ABCD with the following coordinates is a parallelogram, rectangle, or
rhombus, or square. You must prove your answer and explain your reasoning. (2 points each)
A(–4, 2), B(–1,4), C(1,1), D(–2, –1)
a. Is it a parallelogram?
 4  1 2  1 
AC : 
,
  1.5,1.5 
2 
 2
 1  2 4  1 
BD : 
,
  1.5,1.5 
2 
 2
y
Yes, the diagonals
bisect each other since
they have the same
midpoint
5
4
3
2
1
–5
–4
–3
–2
–1
–1
–2
–3
b. Is it a rectangle?
42
2
AB :

1  ( 4) 3
1 4
3
BC :

1  ( 1) 2
Yes, it’s a parallelogram
with one right angles
(since the slopes are
opposite reciprocals)
c. Is it a rhombus?
1 2
1
AC :

1  ( 4) 5
1  4
5 5
BD :


2  ( 1) 1 1
Yes, it’s a parallelogram
with diagonals
perpendicular (since the
slopes are opposite
reciprocals)
d. Is it a square?
Yes, because it’s a
rectangle and a
rhombus
–4
–5
1
2
3
4
5
x
BONUS:
1. Three vertices of parallelogram ABCD are A(–4,–3), B(1,5), and C(8,6). Find the coordinates
of vertex D. (2 points)
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
2. An interior angle of a regular convex polygon is 144 degrees. How many sides does the
polygon have? (2 points)
3. Ima Smartalek claims that any quadrilateral with perpendicular diagonals has to be a rhombus.
Draw a figure (neatly!) that proves him wrong. Use the graph if you want, or blank space on
your paper. (2 points)
y
8
6
4
2
–8
–6
–4
–2
–2
–4
–6
–8
2
4
6
8 x