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

Last updated about 4 years ago

29 questions

Note from the author:

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

Last updated about 4 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.

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G.CO.11

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

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

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G.SRT.5

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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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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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G.CO.11

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G.SRT.5

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

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

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Reflection: Math Success

G.CO.11

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.

10

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

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.

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G.CO.11

G.SRT.5

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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.

G.CO.11

G.SRT.5

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G.CO.11

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G.CO.11

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.

Rhombuses

Rectangles

Squares

None of these

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

10

Find the value of a.
Enter only a number.

10

Find the value of b.
Enter only a number.

10

Find the value of m.
Enter only a number.

10

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 ?

triangle

quadrilateral

pentagon

hexagon

Use Your Vocabulary: Which polygon has two diagonals ?

triangle

quadrilateral

pentagon

hexagon

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.

AFEO

BCDG

GDHO

GJFL

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

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.

Problem 2 Got It?

A

B

C

D

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

Rhombus

Rectangle

Square

None of these

Explain your response to the previous item.

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

Rhombus

Rectangle

Square

None of these

Explain your response to the previous item.

A

B

C

D

A

B

C

D

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

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

Rhombuses

Rectangles

Squares

None of these

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

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.

Use Your Vocabulary: Which polygon has no diagonal ?

triangle

quadrilateral

pentagon

hexagon

Use Your Vocabulary: Which polygon has two diagonals ?

triangle

quadrilateral

pentagon

hexagon

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

AFEO

BCDG

GDHO

GJFL

Problem 2 Got It?

A

B

C

D

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

Rhombus

Rectangle

Square

None of these

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

Rhombus

Rectangle

Square

None of these

A

B

C

D

A

B

C

D

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

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

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

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

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

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.

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.

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

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

Reflection: Math Success

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 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 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

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

Problem 2 Got It?

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.

Explain your response to the previous item.

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.

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.

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 b.
Enter only a number.

Find the value of m.
Enter only a number.

Find the value of n.
Enter only a number.