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Geometry 6-5 Complete Lesson: Conditions for Rhombuses, Rectangles, and Squares

By Matt Richardson
Last updated about 3 years ago
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.

Solve It! Which vertices form a square? Select all that apply.

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?

Problem 1 Got It? Explain your response on the previous item.

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?

Problem 1 Got It? Explain your response on the previous item.

Problem 2 Got It?

Problem 3 Got It? Can you adapt the method in Problem 3 slightly to stake off a square play area? Explain.

Based on the given information, what are the possible classifications for the parallelogram?
Select all that apply.

Explain your response to the previous item.

Based on the given information, what are the possible classifications of the parallelogram?
Select all that apply.

Explain your response to the previous item.

Identify the special parallelograms that have each property.

  • Rhombuses
  • Rectangles
  • Squares
  • Diagonals are perpendicular
  • Diagonals are congruent
  • Diagonals are angle bisectors
  • Diagonals bisect each other
  • Diagonals are perpendicular bisectors of each other

Error Analysis: Your friend says, "A parallelogram with perpendicular diagonals is a rectangle." What is your friend's error? Explain.

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.

Reasoning: Which types of quadrilaterals are possible in the previous item? Select all that apply.

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.)

  • 58
  • 26
  • 90
  • 57
  • 128
  • 66
  • ∠A
  • ∠B
  • ∠C
  • ∠D
  • ∠E
  • ∠F
  • ∠G
  • ∠H
  • ∠I

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.

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

Find the value of a.
Enter only a number.

Find the value of b.
Enter only a number.

Find the value of m.
Enter only a number.

Find the value of n.
Enter only a number.

Vocabulary Review: Cross out the figure that is NOT a quadrilateral.

Use Your Vocabulary: Which polygon has no diagonal ?

Use Your Vocabulary: Which polygon has two diagonals ?

Use Your Vocabulary: Draw the diagonals from one vertex in each figure.

Reflection: Math Success