Geometry 6-8 Complete Lesson: Applying Coordinate Geometry

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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.GPE.4

Geometry 6-8 Complete Lesson: Applying Coordinate Geometry

Geometry 6-8 Complete Lesson: Applying Coordinate Geometry

Solve It! The points shown are three vertices of a parallelogram. Draw all the possible locations of D, the fourth vertex?

Problem 1 Got It?

Problem 1 Got It?

Problem 2 Got It. The diagram shows a trapezoid with the base centered at the origin. Is the trapezoid isosceles? Explain.

Problem 3 Got It? Plan a coordinate proof of the Triangle Midsegment Theorem (Theorem 5-1).

Reasoning: How do variable coordinates generalize figures in the coordinate plane? For example, what do you know about (3, a), (b, -5), etc.

Reasoning: A vertex of a quadrilateral has coordinates (a, b). The x-coordinates of the other three vertices are a or -a and the y-coordinates are b or -b. What kind of quadrilateral is the figure? Be as specific as possible.

Error Analysis: A classmate says the endpoints of the midsegment of the trapezoid in Problem 3 are as follows.
What is your classmate's error? Explain.

Review Lesson 6-7: Let X(-2, 3), Y(5, 5), and Z(4, 10) be the vertices of a triangle. Is △XYZ a right triangle? Explain.

Review Lesson 2-2: Write the inverse of the statement.
If x = 51, then 2x = 102.

Review Lesson 2-2: Write the converse of the statement.
If x = 51, then 2x = 102.

Review Lesson 2-2: Write the contrapositive of the statement.
If x = 51, then 2x = 102.

Review Lesson 3-7: Find and graph the equation of the line that contains the origin and (4, 5).

Review Lesson 3-7: Find the equation of the line that contains (p, q) and has slope a/b.

Vocabulary Review: Categorize each statement as true or false.

Use Your Vocabulary: Match each point with its coordinates.

Reflection: Math Success

Solve It! The points shown are three vertices of a parallelogram. Draw all the possible locations of D, the fourth vertex?

Problem 1 Got It?

Problem 1 Got It?

Problem 2 Got It. The diagram shows a trapezoid with the base centered at the origin. Is the trapezoid isosceles? Explain.

Problem 3 Got It? Plan a coordinate proof of the Triangle Midsegment Theorem (Theorem 5-1).

Reasoning: How do variable coordinates generalize figures in the coordinate plane? For example, what do you know about (3, a), (b, -5), etc.

Reasoning: A vertex of a quadrilateral has coordinates (a, b). The x-coordinates of the other three vertices are a or -a and the y-coordinates are b or -b. What kind of quadrilateral is the figure? Be as specific as possible.

Error Analysis: A classmate says the endpoints of the midsegment of the trapezoid in Problem 3 are as follows.
What is your classmate's error? Explain.

Review Lesson 6-7: Let X(-2, 3), Y(5, 5), and Z(4, 10) be the vertices of a triangle. Is △XYZ a right triangle? Explain.

Review Lesson 2-2: Write the inverse of the statement.
If x = 51, then 2x = 102.

Review Lesson 2-2: Write the converse of the statement.
If x = 51, then 2x = 102.

Review Lesson 2-2: Write the contrapositive of the statement.
If x = 51, then 2x = 102.

Review Lesson 3-7: Find and graph the equation of the line that contains the origin and (4, 5).

Review Lesson 3-7: Find the equation of the line that contains (p, q) and has slope a/b.

Vocabulary Review: Categorize each statement as true or false.

Use Your Vocabulary: Match each point with its coordinates.

Reflection: Math Success

Geometry 6-8 Complete Lesson: Applying Coordinate Geometry

Geometry 6-8 Complete Lesson: Applying Coordinate Geometry

Solve It! The points shown are three vertices of a parallelogram. Draw all the possible locations of D, the fourth vertex?

Problem 1 Got It?

Problem 1 Got It?

Problem 2 Got It. The diagram shows a trapezoid with the base centered at the origin. Is the trapezoid isosceles? Explain.

Problem 3 Got It? Plan a coordinate proof of the Triangle Midsegment Theorem (Theorem 5-1).

Reasoning: How do variable coordinates generalize figures in the coordinate plane? For example, what do you know about (3, a), (b, -5), etc.

Reasoning: A vertex of a quadrilateral has coordinates (a, b). The x-coordinates of the other three vertices are a or -a and the y-coordinates are b or -b. What kind of quadrilateral is the figure? Be as specific as possible.

Error Analysis: A classmate says the endpoints of the midsegment of the trapezoid in Problem 3 are as follows. What is your classmate's error? Explain.

Review Lesson 6-7: Let X(-2, 3), Y(5, 5), and Z(4, 10) be the vertices of a triangle. Is △XYZ a right triangle? Explain.

Review Lesson 2-2: Write the inverse of the statement.If x = 51, then 2x = 102.

Review Lesson 2-2: Write the converse of the statement.If x = 51, then 2x = 102.

Review Lesson 2-2: Write the contrapositive of the statement.If x = 51, then 2x = 102.

Review Lesson 3-7: Find and graph the equation of the line that contains the origin and (4, 5).

Review Lesson 3-7: Find the equation of the line that contains (p, q) and has slope a/b.

Vocabulary Review: Categorize each statement as true or false.

Use Your Vocabulary: Match each point with its coordinates.

Reflection: Math Success

Solve It! The points shown are three vertices of a parallelogram. Draw all the possible locations of D, the fourth vertex?

Problem 1 Got It?

Problem 1 Got It?

Problem 2 Got It. The diagram shows a trapezoid with the base centered at the origin. Is the trapezoid isosceles? Explain.

Problem 3 Got It? Plan a coordinate proof of the Triangle Midsegment Theorem (Theorem 5-1).

Reasoning: How do variable coordinates generalize figures in the coordinate plane? For example, what do you know about (3, a), (b, -5), etc.

Reasoning: A vertex of a quadrilateral has coordinates (a, b). The x-coordinates of the other three vertices are a or -a and the y-coordinates are b or -b. What kind of quadrilateral is the figure? Be as specific as possible.

Error Analysis: A classmate says the endpoints of the midsegment of the trapezoid in Problem 3 are as follows. What is your classmate's error? Explain.

Review Lesson 6-7: Let X(-2, 3), Y(5, 5), and Z(4, 10) be the vertices of a triangle. Is △XYZ a right triangle? Explain.

Review Lesson 2-2: Write the inverse of the statement.If x = 51, then 2x = 102.

Review Lesson 2-2: Write the converse of the statement.If x = 51, then 2x = 102.

Review Lesson 2-2: Write the contrapositive of the statement.If x = 51, then 2x = 102.

Review Lesson 3-7: Find and graph the equation of the line that contains the origin and (4, 5).

Review Lesson 3-7: Find the equation of the line that contains (p, q) and has slope a/b.

Vocabulary Review: Categorize each statement as true or false.

Use Your Vocabulary: Match each point with its coordinates.

Reflection: Math Success

Error Analysis: A classmate says the endpoints of the midsegment of the trapezoid in Problem 3 are as follows.
What is your classmate's error? Explain.

Review Lesson 2-2: Write the inverse of the statement.
If x = 51, then 2x = 102.

Review Lesson 2-2: Write the converse of the statement.
If x = 51, then 2x = 102.

Review Lesson 2-2: Write the contrapositive of the statement.
If x = 51, then 2x = 102.

Error Analysis: A classmate says the endpoints of the midsegment of the trapezoid in Problem 3 are as follows.
What is your classmate's error? Explain.

Review Lesson 2-2: Write the inverse of the statement.
If x = 51, then 2x = 102.

Review Lesson 2-2: Write the converse of the statement.
If x = 51, then 2x = 102.

Review Lesson 2-2: Write the contrapositive of the statement.
If x = 51, then 2x = 102.