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In the parallelogram shown, AE = t + 2, CE = 3t − 14, and DE = 2t + 8. What is the length of line segment DB? |
48 units |
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EFGH is a rhombus. Given EG = 16 and FH = 12, what is the length of one side of the rhombus? |
10 units |
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Figure ABCD is a parallelogram. What is the value of x? |
7 |
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In parallelogram LMNO, MP = 21 m, LP = (y + 3) m, NP = (3y – 1) m, and What are the values of x and y? |
x = 11 m, y = 2 m |
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In quadrilateral ABDC, AB ∥ CD. Which additional piece of information is needed to determine that ABDC is a parallelogram? |
AC ≅ BD |
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ABCD is a square. What is the measure of angle BAC? |
45° |
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Complete the proof to show that ABCD is a parallelogram. The slope of BC is . |
slopes of opposite sides are equal |
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In the diagram, SR = 4√2 and QR = √10. What is the perimeter of parallelogram PQRS? |
8√2 + 2√10 units |
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In parallelogram WXYZ, what is CY? |
15 |
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Figure CDEF is a parallelogram. What is the value of r? |
5 |
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The perimeter of a square is 56 cm. What is the approximate length of its diagonal? |
19.8 cm |
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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. |
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What are the missing angle measures in parallelogram RSTU? |
m∠R = 110°, m∠T = 110°, m∠U = 70° |
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What is the perimeter of rectangle EFGH? |
2√10 + 2√29 units |
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A partial proof was constructed given that MNOP is a parallelogram. By the definition of a parallelogram, 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 |
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Rhombus LMNO is shown with its diagonals. Angle MNO measures 112°. What is the measure of angle LMN? |
68° |
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LMNP is a parallelogram. What additional information would prove that LMNP is a rectangle? |
LP ⊥ PN |
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A rectangle has a width of 9 units and a length of 40 units. What is the length of a diagonal? |
41 units |
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Figure ABCD is a parallelogram. What is the perimeter of ABCD? |
44 units |
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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. |
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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. |
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The perimeter of square JKLM is 48 units. What is the value of x? |
9 |
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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. |
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Which statement proves that quadrilateral JKLM is a kite? |
LM = JM = 3 and JK = LK = √17 |
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What is the measure of angle L in parallelogram LMNO? |
40 |
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