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Geometry 6-5 Conditions for Rhombuses, Rectangles, and Squares
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by Matthew Richardson
| 29 Questions
Note from the author:
A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.
The outlined content above was added from outside of Formative.
The outlined content above was added from outside of Formative.
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1
10 pts
Solve It! Which vertices form a square? Select all that apply.
AFEO
BCDG
GDHO
GJFL
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2
10 pts
Problem 1 Got It? A parallelogram has angle measures of 20, 160, 20, and 160. Can it be a rhombus, a rectangle, or a square?
Rhombus
Rectangle
Square
3
10 pts
Problem 1 Got It? Explain your response on the previous item.
4
10 pts
Problem 1 Got It? Reasoning: Suppose the diagonals of a quadrilateral bisect each other. Can you conclude that it is a rhombus, a rectangle, or a square?
Rhombus
Rectangle
Square
The quadrilateral is none of these.
There is not enough information to make a conclusion.
5
10 pts
Problem 1 Got It? Explain your response on the previous item.
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6
10 pts
Problem 2 Got It?
A
B
C
D
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7
10 pts
Problem 3 Got It? Can you adapt the method in Problem 3 slightly to stake off a square play area? Explain.
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8
10 pts
Based on the given information, what are the possible classifications for the parallelogram?
Select all that apply.
Rhombus
Rectangle
Square
None of these
9
10 pts
Explain your response to the previous item.
10
10 pts
Based on the given information, what are the possible classifications of the parallelogram?
Select all that apply.
Rhombus
Rectangle
Square
None of these
11
10 pts
Explain your response to the previous item.
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12
10 pts
A
B
C
D
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13
10 pts
A
B
C
D
14
10 pts
Identify the special parallelograms that have each property.
  • Diagonals are perpendicular
    Answer by dragging items here
  • Diagonals are congruent
    Answer by dragging items here
  • Diagonals are angle bisectors
    Answer by dragging items here
  • Diagonals bisect each other
    Answer by dragging items here
  • Diagonals are perpendicular bisectors of each other
    Answer by dragging items here
15
10 pts
Error Analysis: Your friend says, "A parallelogram with perpendicular diagonals is a rectangle." What is your friend's error? Explain.
16
10 pts
Reasoning: Complete the following steps on the canvas.
1. Draw a circle and two of its diameters.
2. Connect the endpoints of the diameters to form a quadrilateral.
17
10 pts
Reasoning: Which types of quadrilaterals are possible in the previous item? Select all that apply.
Rhombuses
Rectangles
Squares
None of these
18
10 pts
Review Lesson 6-4: Use the parallelograms in the diagrams above to match the measures with their angles.

(Tip: You may need to use the down arrow key to drag items to the lowest angle measures.)
  • ∠A
    Answer by dragging items here
  • ∠B
    Answer by dragging items here
  • ∠C
    Answer by dragging items here
  • ∠D
    Answer by dragging items here
  • ∠E
    Answer by dragging items here
  • ∠F
    Answer by dragging items here
  • ∠G
    Answer by dragging items here
  • ∠H
    Answer by dragging items here
  • ∠I
    Answer by dragging items here
19
10 pts
Review Lesson 2-3: Write the two conditionals as a biconditional.

If a parallelogram is a rhombus, then its diagonals are perpendicular.
If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
20
10 pts
Review Lesson 2-3: Write the two conditionals as a biconditional.

If a parallelogram is a rectangle, then its diagonals are congruent.
If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
Review Lesson 1-3
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21
10 pts
Find the value of a.
Enter only a number.
22
10 pts
Find the value of b.
Enter only a number.
23
10 pts
Find the value of m.
Enter only a number.
24
10 pts
Find the value of n.
Enter only a number.
25
10 pts
Vocabulary Review: Cross out the figure that is NOT a quadrilateral.
26
10 pts
Use Your Vocabulary: Which polygon has no diagonal ?
triangle
quadrilateral
pentagon
hexagon
27
10 pts
Use Your Vocabulary: Which polygon has two diagonals ?
triangle
quadrilateral
pentagon
hexagon
28
10 pts
Use Your Vocabulary: Draw the diagonals from one vertex in each figure.
29
10 pts
Reflection: Math Success
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