question

In the parallelogram shown, AE = t + 2, CE = 3t âˆ’ 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 âˆ¥ CD. Which additional piece of information is needed to determine that ABDC is a parallelogram?

answer

AC â‰… BD

question

ABCD is a square.
What is the measure of angle BAC?

answer

45Â°

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 âˆ¥ AD and CD âˆ¥ 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 = 4âˆš2 and QR = âˆš10. What is the perimeter of parallelogram PQRS?

answer

8âˆš2 + 2âˆš10 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

mâˆ R = 110Â°, mâˆ T = 110Â°, mâˆ U = 70Â°

question

What is the perimeter of rectangle EFGH?

answer

2âˆš10 + 2âˆš29 units

question

A partial proof was constructed given that MNOP is a parallelogram.
By the definition of a parallelogram,
MN âˆ¥ PO and MP âˆ¥ NO.
Using MP as a transversal, âˆ M and âˆ P are same-side interior angles, so they are supplementary.
Using NO as a transversal, âˆ N and âˆ O are same-side interior angles, so they are supplementary.
Using OP as a transversal, âˆ O and âˆ 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

âˆ M â‰… âˆ O; âˆ N â‰… âˆ P

question

Rhombus LMNO is shown with its diagonals.
Angle MNO measures 112Â°. What is the measure of angle LMN?

answer

68Â°

question

LMNP is a parallelogram.
What additional information would prove that LMNP is a rectangle?

answer

LP âŠ¥ 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 = 60Â°
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 = âˆš17

question

What is the measure of angle L in parallelogram LMNO?

answer

40