This is Just a Test!

Unit 02d: Quadrilaterals (PAP Geometry)
This is Just a
Test!
Name:
Block:
1.
Q1-Q5
OBJ: You will be able to find the sum of the measures of the interior and exterior angles in any -gon
Archaeologist Ertha Diggs has uncovered a piece of a ceramic 2. ABCDE is a regular pentagon. ABFG is a square. What is the
plate. The original plate appears to have been in the shape
value of x?
of a regular polygon. If the original plate was a regular 12gon, it was probably a ceremonial dish from the third
century. If it was a regular 18-gon, it was probably a palace
dinner plate from the twelfth century. Ertha measures each
of the sides of her piece and finds that each side has the
same length. She then conjectures that all the sides of the
original whole plate had the same length. She measures
each of the angles of her piece and finds that they all have
the same measure. She then conjectures that all the angles
of the original whole plate had equal measures. If each
a) ABCDEF is a regular hexagon. ABGH is a square. What
angle measures 150, from what century did the plate
is the value of x?
originate?
a) A regular polygon has an interior angle measure of 144.
How many sides does it have?
b) An equiangular polygon has an interior angle measure of
165. How many sides does it have?
b) MACEWIN is a regular heptagon and DUMN is a square.
What are the values of and ?
E
C
W
z
U
D
x
A
I
N
M
3.
̅̅̅̅ is the side of an equilateral triangle. ̅̅̅̅ is the side of a
square. ̅̅̅̅ is the side of a regular pentagon. ̅̅̅̅ is the side
of a regular hexagon. ̅̅̅̅ is the side of a regular octagon.
Find the following angle measures.
4.
Three regular polygons meet at point A. Only four sides of
the third polygon are visible. How many sides does this
polygon have? Explain your reasoning.
A
a)
Notice that the sum of the three angles surrounding
point A sum to 360. Find 3 different regular polygons
such that the sum of an interior angle from each totals
360 similar to the problem above.
b) Repeat part a) but this time find 4 different regular
polygons such that the sum of an interior angle from
each totals 360.
5.
Find the measure of each lettered angle.
a)
Find the measure of each lettered angle.
a
c
b
d
e
f
h
g
b) Find the measure of each lettered angle.
OBJ: You will be able to discover and use properties of kites
OBJ: You will be able to find the area of kites
7. Kenny says that you can find all four of the measure of the
WEST is a kite. Find mS.
interior angles of a kite if you knew any two of them. Draw
a counterexample to disprove Kenny’s conjecture.
a) Find the value of .
Q6-Q8
6.
x
a) Purple Geometry Textbook P. 547:18
b) Purple Geometry Textbook P. 547:19
95°
95°
b) Purple Geometry Textbook P. 547:33
8.
Find the perimeter and area of the kite.
a) Purple Geometry Textbook P. 547:22
b) Purple Geometry Textbook P. 547:23
OBJ: You will be able to discover and use properties of trapezoids
OBJ: You will be able to find the area of trapezoids
You’ve been asked to build a window frame for a hexagonal 10. x =
window. To make the frame, you’ll cut identical trapezoidal
pieces. At what angles a and b should you cut the frame?
Q9-Q12
9.
a) Purple Geometry Textbook P. 546: 7
b) Purple Geometry Textbook P. 546: 8
11. Approximate the area of the figure below by subdividing it
into two trapezoids.
a) Purple Geometry Textbook P. 547: 26
b) Purple Geometry Textbook P. 547: 27
12. The midsegment of a triangle divides the triangle into a
triangle and a trapezoid. If the original triangle has an area
2
of 64 in , what is the area of the trapezoid?
M
L
N
a)
K
a)
In the figure above, the area
area of
.
b) In the figure above, the area of
the area of
.
b)
O
is 24 u2. Find the
is 105 u2. Find
Q13-Q14
OBJ: You will be able to discover and use properties of parallelograms
13. Find point L such that PARL is a parallelogram.
14. Find the value of each variable in the parallelogram
x=
y=
Show Objects
10
8
P
6
4
R
2
A
5
a) Purple Geometry Textbook P. 518: 7
b) Purple Geometry Textbook P. 518: 8
10
a) Purple Geometry Textbook P. 519: 37
b) Purple Geometry Textbook P. 532: 4
OBJ: You will be able to discover and use properties of rhombuses, rectangles, and squares
OBJ: You will be able to find the area of rhombuses, rectangles, and squares
15. Classify the special quadrilateral. Then find the values of x
16. Classify the special quadrilateral. Then find the values of x
and y.
and y.
Classification:
Classification:
x=
x=
y=
y=
Q15-Q20
a) Purple Geometry Textbook P. 538: 28
b) Purple Geometry Textbook P. 555: 20
17. A =
a) Purple Geometry Textbook P. 538: 26
b) Purple Geometry Textbook P. 538: 29
18. The rectangle below has an area of 65. What is the value of
x?
x=
x-4
x+4
a) Purple Geometry Textbook P. 734: 20
b) A =
a)
The rectangle below has an area of 60. What is the
value of x?
8
x 15
6
4
x + 13
2
b) The rectangle below has an area of 56. What is the
value of x?
5
2
x 5
4
x+5
19. PQRS is a square. Find the coordinates of S and R.
20. ABCD is a rectangle. Find the coordinates of B and D.
C (6, 7)
D
B
A (2, 0)
a)
is a square. Find the coordinates of
and .
a)
is a rectangle. Find the coordinates for
and .
D
A
B
E (10, 8)
D
(-1, 2)
C
(0, 3)
C (5, 0)
b)
is a square. Find the coordinates of
F
and .
b)
D
is a rectangle. Find the coordinates for
G
C
(-4, 0)
A
F
(-4, 0)
D (10, -3)
B (0, -6)
E
and .
Q21-Q22
OBJ: You will be able to write indirect proofs
OBJ: You will be able to prove that a quadrilateral is a parallelogram
For Q21-Q22, write a proof. Use the back of this page if you find that you need more space.
B
21. Given: Quadrilateral
22. Given: Quadrilateral
O
C
with midpoints
with
, , , and
N
P
R
Prove:
is not a
Prove:
is a
kite
parallelogram
A
E
T
91°
S
U
D
D
P
a) Purple Geometry Textbook P. 529: 40
b) Purple Geometry Textbook P. 529: 42
a) Given:
Trapezoid
;
Prove:
is not
isosceles
T
P
b) Given:
Quadrilateral
;
Prove:
is not a kite
A
R
R
F
E
T
A