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

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

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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?

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

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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?

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

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Problem 2 Got It?

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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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Explain your response to the previous item.

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Explain your response to the previous item.

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Identify the special parallelograms that have each property.

Rhombuses
Rectangles
Squares

Diagonals are perpendicular
Diagonals are congruent

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

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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.

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

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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.

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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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Find the value of a.
Enter only a number.

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Find the value of b.
Enter only a number.

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

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Use Your Vocabulary: Which polygon has no diagonal ?

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Use Your Vocabulary: Which polygon has two diagonals ?

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

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Reflection: Math Success

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

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.

Explain your response to the previous item.

Explain your response to the previous item.

Identify the special parallelograms that have each property.

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 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.

Find the value of a.Enter only a number.

Find the value of b.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

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.

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.)

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.

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

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

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

Find the value of m.Enter only a number.

Find the value of n.Enter only a number.

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.

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.

Find the value of a.
Enter only a number.

Find the value of b.
Enter only a number.

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

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

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.

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.)

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.

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.

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

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

Find the value of m.
Enter only a number.

Find the value of n.
Enter only a number.