Download ps9parallelograms2015

Quadrilaterals
11/24/14
NAME_________________________
B-block
Part I - Parallelograms
After seeing the GSP demo sketch, you should know the definition and three properties of
parallelograms. Fill in the blanks below, and give an example of each from the figure.
ABCD is a parallelogram
1.
Definition: A parallelogram is a __________________
with both pairs of opposite sides _______________.
For the parallelogram shown, that means:
___________ and ___________
2.
D
A
M
___________ ________ of a parallelogram are congruent.
For the parallelogram shown, that means:
___________ and ___________
C
B
3.
___________ ________ of a parallelogram are congruent.
For the parallelogram shown, that means:
___________ and ___________
4.
The diagonals of a parallelogram ____________ each other.
For the parallelogram shown, that means __________.
Questions # 1-19 refer to parallelogram DECK
1.
2.
3.
4.
5.
6.
7.
8.
If DE = 10 then KC = ____
If DC = 18 then DT = ____
If mLEDK = 100, then mLECK = ____
If mLDEC = 75, then mLKDE = ____
If mL1 = 30 and mL2 = 40, then mLKCE = ____
If mL1 = 30 and mL2 = 40, then mL3 = ____
If mL3 = 36 and mL2 = 44, then mLKDE = ____
If DT = 7 and KT = 9, then CD = ____
C
K
2
1
T
3
D
DECK is a parallelogram
1
E
C
K
Find the value of x or y
2
1
9.
DE = 5x and KC = 3x + 12
x = ____
10.
DK = 2x + 5 and EC = 47 – 4x
x = ____
11.
ET = x + 3 and EK = 22
x = ____
12.
DT = ½ x and TC = 10
x = ____
13.
mLKCE = 6y – 20 and mLDKC = 2y + 80
y = ____
14.
mLDEC = 80 – y and mLDKC = y + 40
y = ____
15.
mL1 = y + 10 and mL2 = 3y and mL3 = ½ y + 15
y = ____
16.
mLDEC = y/4 and mLECK = (y + 60)/2
y = ____
17.
If KT = 2x + y, DT = x + 2y, TE = 12 and TC = 9 then
x = ____ and y = ____
18.
If DE = x + y, EC = 12, CK = 2x – y, KD = 3x – 2y, then
x = ____, y = ____ and the perimeter of parallelogram DECK is ____.
19.
If mL1 = 4x, mL2 = 3x, and mL3 = x2 – 60, then x = ____ and
mLCED = ____
2
T
3
D
E
Fill in the blanks with always, sometimes, or never.
1. The diagonals of a quadrilateral _____________ bisect each other.
2. If the measures of two angles of a quadrilateral are equal, then the quadrilateral is
____________ a parallelogram.
3. If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is
___________ a parallelogram.
4. To prove that a quadrilateral is a parallelogram, it is __________ sufficient to show that
one pair of opposite sides is parallel.
5. If both pairs of opposite angles of a quadrilateral are congruent, the quadrilateral is
____________ a parallelogram.
6. In a quadrilateral, if one pair of opposite sides is parallel and the other pair of opposite
sides is congruent, then the quadrilateral is ___________ a parallelogram.
QUESTIONS 7-8 are the ones I added this year
ABCD is a parallelogram
7. Find the length of AC if DM = 2a , CM = 2a 13 and BM = 14a  196
2
B
A
M
C
D
AC = ______
ABCD is a parallelogram
8. Solve for x and y if:
B
mLBCD = 131
mLCDA = 5x + 3y
mLDAB = 7x + 12y
C
A
D
x = ____ y = ____
3
Part II - Special Parallelograms
A quadrilateral with four right angles is a _______________.
Since both pairs of opposite angles are congruent, a rectangle is also a ________________.
A quadrilateral with four congruent sides is a _____________.
Since both pairs of opposite sides are congruent, a rhombus is also a _________________.
A quadrilateral with four right angles and four congruent sides is called a _____________.
Notice that every square is a special kind of rectangle, as well as a special kind of rhombus.
Rectangles, rhombuses, and squares also have the following special properties.
1. The diagonals of a rectangle are congruent.
Q
R
T
S
What does this mean is true
about rectangle QRST? _______
2. The diagonals of a rhombus are perpendicular
What does this mean is true
about rhombus ABCD?
_______
3. Each diagonal of a rhombus bisects two angles of the rhombus
A
B
D
AC bisects angles ____ and ____
BD bisects angles ____ and ____
A
C
Construct a diagram to help explain why each of the following two theorems is true:
1. If one angle of a parallelogram is a right angle,
then the parallelogram is a rectangle.
2. If two consecutive sides of a parallelogram are congruent,
then the parallelogram is a rhombus.
Quad. ABCD is a rhombus. Find the measure of each angle:
4
B
D
C
1.
2.
3.
4.
5.
6.
LACD = ______
LDEC = ______
LEDC = ______
LEDA = ______
LBCD = ______
LABC = ______
A
B
E
62°
D
C
Check the boxes that apply:
Property
1
2
3
4
5
6
7
8
9
10
Parallelogram Rectangle Rhombus
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent
A diagonal forms two congruent ’s
Diagonals bisect each other
Diagonals are congruent
Diagonals are perpendicular
A diagonal bisects two angles
All angles are right angles
All sides are congruent
5
Square