Quadrilaterals and Coordinate Algebra Unit Test 96%

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?

x = 11 m, y = 2 m

In quadrilateral ABDC, AB ∥ CD. Which additional piece of information is needed to determine that ABDC is a parallelogram?

AC ≅ BD

In parallelogram WXYZ, what is CY?

15

The perimeter of a square is 56 cm. What is the approximate length of its diagonal?

19.8 cm

What is the perimeter of rectangle EFGH?

2√10 + 2√29 units

What is the measure of angle L in parallelogram LMNO?

40

A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal?

41 units

Figure ABCD is a parallelogram. What is the perimeter of ABCD?

44 units

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

45°

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

68°

Figure ABCD is a parallelogram. What is the value of x?

7

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

LP ⊥ PN

What are the missing angle measures in parallelogram RSTU?

m∠R = 110°, m∠T = 110°, m∠U = 70°

In the parallelogram shown, AE = t + 2, CE = 3t − 14, and DE = 2t + 8. What is the length of line segment DB?

48 units

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?

∠M ≅ ∠O; ∠N ≅ ∠P

EFGH is a rhombus. Given EG = 16 and FH = 12, what is the length of one side of the rhombus?

10 units

In the diagram, SR = 4√2 and QR = √10. What is the perimeter of parallelogram PQRS?

8√2 + 2√10 units

The perimeter of square JKLM is 48 units. What is the value of x?

9

Which statement proves that quadrilateral JKLM is a kite?

LM = JM = 3 and JK = LK = √17

Which statement proves that △XYZ is an isosceles right triangle?

The slope of XZ is 3/4, the slope of XY is -4/3, and XZ = XY = 5.

The vertices of a quadrilateral in the coordinate plane are known. How can the perimeter of the figure be found?

Use the distance formula to find the length of each side, and then add the lengths.

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.

a = 60° The perimeter of the rhombus is 16 inches. The length of the longer diagonal is approximately 7 inches.

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.

slopes of opposite sides are equal

Figure CDEF is a parallelogram. What is the value of r?

5

Which statements are true of all squares? Check all that apply.

The diagonals are perpendicular. The diagonals are congruent to each other. The diagonals bisect the vertex angles. The diagonals bisect each other.