Geometry 6-3 Complete Lesson: Proving That a Quadrilateral Is a Parallelogram

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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.

G.CO.11

Review Lessons 5-2 & 6-2

G.CO.11

Geometry 6-3 Complete Lesson: Proving That a Quadrilateral Is a Parallelogram

Geometry 6-3 Complete Lesson: Proving That a Quadrilateral Is a Parallelogram

Solve It! Each section of glass in the exterior of a building in Macau, China, forms an equilateral triangle. Do you think the window washer's feet stay parallel to the ground as he lands at each level of windows? Explain. (Assume that the bases of the lowest triangles are parallel to the ground.)

Problem 1 Got It?

Problem 2 Got It? Can you prove that quadrilateral DEFG is a parallelogram based on the given information? Explain.

Problem 2 Got It? Can you prove that quadrilateral ANDL is a parallelogram based on the given information? Explain.

Problem 3 Got It? Reasoning: What is the maxium height that the vehicle lift can elevate the truck? Explain.

Compare and Contrast: How is Theorem 6-11 in this lesson different from Theorem 6-6 in the previous lesson? In what situations should you use each theorem? Explain.

Error Analysis: Your friend says, "If a quadrilateral has a pair of opposite sides that are congruent and a pair of opposite sides that are parallel, then it is a parallelogram." What is your friend's error? Explain.

Review Lesson 6-2: Use the parallelograms in the diagram above to match the values with the variables.

Review Lessons 4-4 & 4-7: Explain how you can use overlapping triangles to prove the congruence statement.

Vocabulary Review: Does a pentagon have opposite sides?

Vocabulary Review: Does an n-gon have opposite sides if n is an odd number?

Use Your Vocabulary: Classify each statement as parallelogram if it describes a parallelogram. Leave statements that do not represent parallelograms unclassified.

Use Your Vocabulary: Classify the quadrilateral as appearing to be a parallelogram or not appearing to be a parallelogram by writing "parallelogram"or "NP".Do not include spaces in your response.

Use Your Vocabulary: Classify the quadrilateral as appearing to be a parallelogram or not appearing to be a parallelogram by writing "parallelogram"or "NP".Do not include spaces in your response.

Use Your Vocabulary: Classify the quadrilateral as appearing to be a parallelogram or not appearing to be a parallelogram by writing "parallelogram"or "NP".Do not include spaces in your response.

Reflection: Math Success

Solve It! Each section of glass in the exterior of a building in Macau, China, forms an equilateral triangle. Do you think the window washer's feet stay parallel to the ground as he lands at each level of windows? Explain. (Assume that the bases of the lowest triangles are parallel to the ground.)

Problem 1 Got It?

Problem 2 Got It? Can you prove that quadrilateral DEFG is a parallelogram based on the given information? Explain.

Problem 2 Got It? Can you prove that quadrilateral ANDL is a parallelogram based on the given information? Explain.

Problem 3 Got It? Reasoning: What is the maxium height that the vehicle lift can elevate the truck? Explain.

Compare and Contrast: How is Theorem 6-11 in this lesson different from Theorem 6-6 in the previous lesson? In what situations should you use each theorem? Explain.

Error Analysis: Your friend says, "If a quadrilateral has a pair of opposite sides that are congruent and a pair of opposite sides that are parallel, then it is a parallelogram." What is your friend's error? Explain.

Review Lesson 6-2: Use the parallelograms in the diagram above to match the values with the variables.

Review Lessons 4-4 & 4-7: Explain how you can use overlapping triangles to prove the congruence statement.

Enter only a number.

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Vocabulary Review: Does a pentagon have opposite sides?

Vocabulary Review: Does an n-gon have opposite sides if n is an odd number?

Use Your Vocabulary: Classify each statement as parallelogram if it describes a parallelogram. Leave statements that do not represent parallelograms unclassified.

Use Your Vocabulary: Classify the quadrilateral as appearing to be a parallelogram or not appearing to be a parallelogram by writing "parallelogram"or "NP".Do not include spaces in your response.

Use Your Vocabulary: Classify the quadrilateral as appearing to be a parallelogram or not appearing to be a parallelogram by writing "parallelogram"or "NP".Do not include spaces in your response.

Use Your Vocabulary: Classify the quadrilateral as appearing to be a parallelogram or not appearing to be a parallelogram by writing "parallelogram"or "NP".Do not include spaces in your response.

Reflection: Math Success

Enter only a number.

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Enter only a number.

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Enter only a number.

Use Your Vocabulary: Classify each statement as parallelogram if it describes a parallelogram.
Leave statements that do not represent parallelograms unclassified.

Use Your Vocabulary: Classify the quadrilateral as appearing to be a parallelogram or not appearing to be a parallelogram by writing "parallelogram"or "NP".
Do not include spaces in your response.

Use Your Vocabulary: Classify the quadrilateral as appearing to be a parallelogram or not appearing to be a parallelogram by writing "parallelogram"or "NP".
Do not include spaces in your response.

Use Your Vocabulary: Classify the quadrilateral as appearing to be a parallelogram or not appearing to be a parallelogram by writing "parallelogram"or "NP".
Do not include spaces in your response.

Use Your Vocabulary: Classify each statement as parallelogram if it describes a parallelogram.
Leave statements that do not represent parallelograms unclassified.

Use Your Vocabulary: Classify the quadrilateral as appearing to be a parallelogram or not appearing to be a parallelogram by writing "parallelogram"or "NP".
Do not include spaces in your response.

Use Your Vocabulary: Classify the quadrilateral as appearing to be a parallelogram or not appearing to be a parallelogram by writing "parallelogram"or "NP".
Do not include spaces in your response.

Use Your Vocabulary: Classify the quadrilateral as appearing to be a parallelogram or not appearing to be a parallelogram by writing "parallelogram"or "NP".
Do not include spaces in your response.