Download Task on Parallelograms

Task on Parallelograms
Name_________________________
A quadrilateral is a polygon with four sides.
1.
Is a rectangle a type of quadrilateral?
2.
Is a pentagon a type of quadrilateral?
--------------------------------------------------------------------------------------------------------------------Quadrilaterals are named using the four letters of the vertices. The four letters are not given in a
random order. After the first letter of the name is chosen, one must proceed in a clockwise or
counter-clockwise direction around the figure when choosing the other three letters of the name.
For example, if one wishes to name the quadrilateral to the right, and
he/she starts with vertex A and proceeds around the figure in a clockwise
direction, then an appropriate name would be quadrilateral ABCD.
(Make sure you understand the above paragraph.)
B
A
D
An incorrect name starting at vertex A for the quadrilateral to the left
would be quadrilateral ACBD. Do you see how the first two vertices in
the name, A and C, are not "in order" in the figure to the right?
C
--------------------------------------------------------------------------------------------------------------------3.
Provide the name for the quadrilateral to the right if
one starts at vertex H and goes around the figure in a
counter-clockwise direction.
4.
Is "Quadrilateral EHGF" a correct name for the
quadrilateral to the right?
5.
Is "Quadrilateral FGHE" a correct name?
H
E
F
G
--------------------------------------------------------------------------------------------------------------------B
Again, let us consider quadrilateral ABCD from above.
A
A diagonal is a line segment whose endpoints are non-consecutive
vertices of a polygon. "Non-consecutive vertices" simply means
vertices that are not next to each other.
D
C
As you can see, a diagonal for ABCD was constructed by drawing a line segment from
vertex A to vertex C.
6.
A second diagonal could be constructed by connecting which two vertices?
DO NOT DRAW THIS DIAGONAL!
7.
From a previous lesson, what is the sum of the measures of the interior angles of a
triangle?
After drawing the diagonal, two triangles have been formed.
B
A
Since the big quadrilateral is made up of two smaller triangles, then
one could conclude that the sum of the measures of the interior angles
of the big quadrilateral is equal to two times your answer from Question 7.
D
C
8.
What is the sum of the measures of the interior angles of a quadrilateral?
--------------------------------------------------------------------------------------------------------------------A parallelogram is a specific type of quadrilateral. A parallelogram is a quadrilateral in which
both pairs of opposite sides are parallel.
"Opposite sides" are simply the sides which are across from each other. For example, in
Quadrilateral ABCD above, AB and DC are "opposite sides". Obviously, ABCD is not a
parallelogram because AB and DC are not parallel.
9.
What is the other pair of "opposite sides" in Quadrilateral ABCD above?
--------------------------------------------------------------------------------------------------------------------For Questions 10-12, is the figure a parallelogram?
10.
11.
12.
M
P
H
R
S
U
T
E
N
F
O
G
---------------------------------------------------------------------------------------------------------------------
I
J
W
L
K
Y
X
Z
Consider the parallelograms above. For the questions below, measure the segments in
centimeters, and round each answer to the nearest tenth of a centimeter (ex. 2.1 centimeters).
13.
What is the length of IJ ?
15.
What is the length of WX ?
14.
What is the length of LK ?
16.
What is the length of YZ ?
17.
Based on the answers above, complete the following statement: "Opposite sides of a
parallelogram are _______________."
Notes on Parallelograms
Name_________________________
The sum of the measures of the interior angles of a quadrilateral is _____________.
A parallelogram is a quadrilateral in which opposite sides are ______________.
If a quadrilateral is a parallelogram, then opposite sides are _______________.
If a quadrilateral is a parallelogram, then opposite angles are ________________.
If a quadrilateral is a parallelogram, then consecutive angles are ________________.
If a quadrilateral is a parallelogram, then the diagonals ______________ each other.
--------------------------------------------------------------------------------------------------------------------Homework on Parallelograms
For Questions 1-6, consider the parallelogram below.
1.
Provide the two possible four-letter names for the
parallelogram that both begin with the letter U.
2.
Complete the statement: RU is parallel to _________.
S
R
T
3.
Complete the statement: UT is congruent to __________.
4.
True or False: ST must be congruent to UT .
5.
True or False:  R must be congruent to T .
U
6.
What are two possible answers which could be placed in the blank below:
mU  ________  180 ?
---------------------------------------------------------------------------------------------------------------------
7.
Construct parallelogram EGKH on the coordinate plane to the
right so that each vertex is in a different quadrant and so that
vertex E is in Quadrant III.
6
4
2
-5
5
-2
-4
-6
--------------------------------------------------------------------------------------------------------------------8.
Suppose parallelogram MNOP has the following characteristic: mM  75 .
Find the measures of each of the other interior angles. Be sure to be specific (for
example, write mN = _______, and so on).
For Questions 9-12, find the value of the variable in the diagram. Assume all figures are
parallelograms. THIS IS A VERY IMPORTANT SECTION!!!
10. mO  7 y  20 and mP  3 y
9.
4x + 18
O
7y + 20
R
3y
10x + 6
P
Q
11. mH  5z  8 and mI  9z  42
12. CE  2k 1 and EB  5k 19
A
H
5z + 8
5k - 19
L
2k - 1
B
E
C
J
9z - 42
I
D
--------------------------------------------------------------------------------------------------------------------13.
Consider parallelogram ABDC from Question 12 above. Suppose that
AE  24 centimeters . What is AD?
--------------------------------------------------------------------------------------------------------------------14.
A quadrilateral has three interior angles with measures of 49 , 111 , and 133 . What is
the measure of the fourth interior angle?
--------------------------------------------------------------------------------------------------------------------15.
In a rectangle (a type of quadrilateral), all four interior angles have the same measure.
What is the measure of each interior angle?
--------------------------------------------------------------------------------------------------------------------16.
Is a rectangle a type of parallelogram? Is a square a type of parallelogram?
--------------------------------------------------------------------------------------------------------------------17.
Parallelogram WYXZ is constructed such that ZW = 31 inches, and WY = 22 inches.
What is XZ? What is YX?
Answer Sheet on Task on Parallelograms
Name_________________________
1.______________________
10. ______________________
2. ______________________
11. ______________________
3. ______________________
12. ______________________
4. ______________________
13. ______________________
5. ______________________
14. ______________________
6. ______________________
15. ______________________
7. ______________________
16. ______________________
8. ______________________
17. ______________________
9. ______________________
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