In the parallelogram shown, AE = t + 2, CE = 3t − 14, and DE = 2t + 8.
What is the length of line segment DB?
answer
48 units
question
EFGH is a rhombus.
Given EG = 16 and FH = 12, what is the length of one side of the rhombus?
answer
10 units
question
Figure ABCD is a parallelogram.
What is the value of x?
answer
7
question
In parallelogram LMNO, MP = 21 m, LP = (y + 3) m, NP = (3y - 1) m, and
OP = (2x - 1) m.
What are the values of x and y?
answer
x = 11 m, y = 2 m
question
In quadrilateral ABDC, AB ∥ CD. Which additional piece of information is needed to determine that ABDC is a parallelogram?
answer
AC ≅ BD
question
ABCD is a square.
What is the measure of angle BAC?
answer
45°
question
Complete the proof to show that ABCD is a parallelogram.
The slope of BC is .
The slope of AD is .
The slope of CD is .
The slope of BA is .
BC ∥ AD and CD ∥ BA because the __________________________________. Therefore, ABCD is a parallelogram because both pairs of opposite sides are parallel.
answer
slopes of opposite sides are equal
question
In the diagram, SR = 4√2 and QR = √10. What is the perimeter of parallelogram PQRS?
answer
8√2 + 2√10 units
question
In parallelogram WXYZ, what is CY?
answer
15
question
Figure CDEF is a parallelogram.
What is the value of r?
answer
5
question
The perimeter of a square is 56 cm. What is the approximate length of its diagonal?
answer
19.8 cm
question
Which statement proves that â–³XYZ is an isosceles right triangle?
answer
The slope of XZ is 3/4, the slope of XY is -4/3, and XZ = XY = 5.
question
What are the missing angle measures in parallelogram RSTU?
answer
m∠R = 110°, m∠T = 110°, m∠U = 70°
question
What is the perimeter of rectangle EFGH?
answer
2√10 + 2√29 units
question
A partial proof was constructed given that MNOP is a parallelogram.
By the definition of a parallelogram,
MN ∥ PO and MP ∥ NO.
Using MP as a transversal, ∠M and ∠P are same-side interior angles, so they are supplementary.
Using NO as a transversal, ∠N and ∠O are same-side interior angles, so they are supplementary.
Using OP as a transversal, ∠O and ∠P are same-side interior angles, so they are supplementary.
Therefore, __________ and _________ because they are supplements of the same angle.
Which statements should fill in the blanks in the last line of the proof?
answer
∠M ≅ ∠O; ∠N ≅ ∠P
question
Rhombus LMNO is shown with its diagonals.
Angle MNO measures 112°. What is the measure of angle LMN?
answer
68°
question
LMNP is a parallelogram.
What additional information would prove that LMNP is a rectangle?
answer
LP ⊥ PN
question
A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal?
answer
41 units
question
Figure ABCD is a parallelogram.
What is the perimeter of ABCD?
answer
44 units
question
The vertices of a quadrilateral in the coordinate plane are known. How can the perimeter of the figure be found?
answer
Use the distance formula to find the length of each side, and then add the lengths.
question
Which statements are true of all squares? Check all that apply.
answer
The diagonals are perpendicular.
The diagonals are congruent to each other.
The diagonals bisect the vertex angles.
The diagonals bisect each other.
question
The perimeter of square JKLM is 48 units.
What is the value of x?
answer
9
question
A quilt piece is designed with four congruent triangles to form a rhombus so that one of the diagonals is equal to the side length of the rhombus.
Which measures are true for the quilt piece? Check all that apply.
answer
a = 60°
The perimeter of the rhombus is 16 inches.
The length of the longer diagonal is approximately 7 inches.
question
Which statement proves that quadrilateral JKLM is a kite?
answer
LM = JM = 3 and JK = LK = √17
question
What is the measure of angle L in parallelogram LMNO?
answer
40
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