Geometry 6-7 Complete Lesson: Polygons in the Coordinate Plane

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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.

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Geometry 6-7 Complete Lesson: Polygons in the Coordinate Plane

Geometry 6-7 Complete Lesson: Polygons in the Coordinate Plane

Solve It! You and a friend are playing a board game. Players place rubber bands on their own square grid to form different shapes. The object of the game is to guess the vertices of your opponent's shape. How would you place pieces on the grid to complete a right isosceles triangle?

Solve It! Refer to your sketch in the previous item and justify the placement of each rubber band that you added.

Problem 1 Got It?

Problem 2 Got It? ▱ MNPQ has vertices M(0, 1), N(-1, 4), P(2, 5), and Q(3, 2).
a. Is ▱ MNPQ a rectangle? Explain.

Problem 2 Got It? ▱ MNPQ has vertices M(0, 1), N(-1, 4), P(2, 5), and Q(3, 2).
b. Is ▱ MNPQ a square? Explain.

Problem 3 Got It?

Writing: Describe how you would determine whether the lengths of the medians from the base angles D and F are congruent.

Error Analysis: A student says that the quadrilateral with vertices D(1, 2), E(0, 7), F(5, 6), and G(7, 0) is a rhombus because its diagonals are perpendicular. What is the student's error?

Review Lesson 6-6: Refer to the isosceles trapezoid shown. Find the value of x.

Review Lesson 5-3: Find the circumcenter of △ABC.

Review Lesson 3-7: Identify the slope of each segment, whose endpoints are given. Not all slopes will be used.

Vocabulary Review: Identify each item labeled on the coordinate plane. Use the arrow keys to access items, if necessary.

Use Your Vocabulary: Complete each statement with the correct word. Use each word only once.

Reflection: Math Success

Solve It! You and a friend are playing a board game. Players place rubber bands on their own square grid to form different shapes. The object of the game is to guess the vertices of your opponent's shape. How would you place pieces on the grid to complete a right isosceles triangle?

Solve It! Refer to your sketch in the previous item and justify the placement of each rubber band that you added.

Problem 1 Got It?

Problem 2 Got It? ▱ MNPQ has vertices M(0, 1), N(-1, 4), P(2, 5), and Q(3, 2).
a. Is ▱ MNPQ a rectangle? Explain.

Problem 2 Got It? ▱ MNPQ has vertices M(0, 1), N(-1, 4), P(2, 5), and Q(3, 2).
b. Is ▱ MNPQ a square? Explain.

Problem 3 Got It?

Writing: Describe how you would determine whether the lengths of the medians from the base angles D and F are congruent.

Error Analysis: A student says that the quadrilateral with vertices D(1, 2), E(0, 7), F(5, 6), and G(7, 0) is a rhombus because its diagonals are perpendicular. What is the student's error?

Review Lesson 6-6: Refer to the isosceles trapezoid shown. Find the value of x.

Review Lesson 6-6: Refer to the isosceles trapezoid shown. Find m∠1. Enter only a number.

Review Lesson 6-6: Refer to the isosceles trapezoid shown. Find m∠2. Enter only a number.

Review Lesson 6-6: Refer to the isosceles trapezoid shown. Find m∠3. Enter only a number.

Review Lesson 5-3: Find the circumcenter of △ABC.

Review Lesson 3-7: Identify the slope of each segment, whose endpoints are given. Not all slopes will be used.

Vocabulary Review: Identify each item labeled on the coordinate plane. Use the arrow keys to access items, if necessary.

Use Your Vocabulary: Complete each statement with the correct word. Use each word only once.

Reflection: Math Success

Review Lesson 6-6: Refer to the isosceles trapezoid shown. Find m∠1. Enter only a number.

Review Lesson 6-6: Refer to the isosceles trapezoid shown. Find m∠2. Enter only a number.

Review Lesson 6-6: Refer to the isosceles trapezoid shown. Find m∠3. Enter only a number.

Geometry 6-7 Complete Lesson: Polygons in the Coordinate Plane

Geometry 6-7 Complete Lesson: Polygons in the Coordinate Plane

Solve It! You and a friend are playing a board game. Players place rubber bands on their own square grid to form different shapes. The object of the game is to guess the vertices of your opponent's shape. How would you place pieces on the grid to complete a right isosceles triangle?

Solve It! Refer to your sketch in the previous item and justify the placement of each rubber band that you added.

Problem 1 Got It?

Problem 2 Got It? ▱ MNPQ has vertices M(0, 1), N(-1, 4), P(2, 5), and Q(3, 2). a. Is ▱ MNPQ a rectangle? Explain.

Problem 2 Got It? ▱ MNPQ has vertices M(0, 1), N(-1, 4), P(2, 5), and Q(3, 2). b. Is ▱ MNPQ a square? Explain.

Problem 3 Got It?

Writing: Describe how you would determine whether the lengths of the medians from the base angles D and F are congruent.

Error Analysis: A student says that the quadrilateral with vertices D(1, 2), E(0, 7), F(5, 6), and G(7, 0) is a rhombus because its diagonals are perpendicular. What is the student's error?

Review Lesson 6-6: Refer to the isosceles trapezoid shown. Find the value of x.

Review Lesson 5-3: Find the circumcenter of △ABC.

Review Lesson 3-7: Identify the slope of each segment, whose endpoints are given. Not all slopes will be used.

Vocabulary Review: Identify each item labeled on the coordinate plane. Use the arrow keys to access items, if necessary.

Use Your Vocabulary: Complete each statement with the correct word. Use each word only once.

Reflection: Math Success

Solve It! You and a friend are playing a board game. Players place rubber bands on their own square grid to form different shapes. The object of the game is to guess the vertices of your opponent's shape. How would you place pieces on the grid to complete a right isosceles triangle?

Solve It! Refer to your sketch in the previous item and justify the placement of each rubber band that you added.

Problem 1 Got It?

Problem 2 Got It? ▱ MNPQ has vertices M(0, 1), N(-1, 4), P(2, 5), and Q(3, 2). a. Is ▱ MNPQ a rectangle? Explain.

Problem 2 Got It? ▱ MNPQ has vertices M(0, 1), N(-1, 4), P(2, 5), and Q(3, 2). b. Is ▱ MNPQ a square? Explain.

Problem 3 Got It?

Writing: Describe how you would determine whether the lengths of the medians from the base angles D and F are congruent.

Error Analysis: A student says that the quadrilateral with vertices D(1, 2), E(0, 7), F(5, 6), and G(7, 0) is a rhombus because its diagonals are perpendicular. What is the student's error?

Review Lesson 6-6: Refer to the isosceles trapezoid shown. Find the value of x.

Review Lesson 6-6: Refer to the isosceles trapezoid shown. Find m∠1. Enter only a number.

Review Lesson 6-6: Refer to the isosceles trapezoid shown. Find m∠2. Enter only a number.

Review Lesson 6-6: Refer to the isosceles trapezoid shown. Find m∠3. Enter only a number.

Review Lesson 5-3: Find the circumcenter of △ABC.

Review Lesson 3-7: Identify the slope of each segment, whose endpoints are given. Not all slopes will be used.

Vocabulary Review: Identify each item labeled on the coordinate plane. Use the arrow keys to access items, if necessary.

Use Your Vocabulary: Complete each statement with the correct word. Use each word only once.

Reflection: Math Success

Review Lesson 6-6: Refer to the isosceles trapezoid shown. Find m∠1. Enter only a number.

Review Lesson 6-6: Refer to the isosceles trapezoid shown. Find m∠2. Enter only a number.

Review Lesson 6-6: Refer to the isosceles trapezoid shown. Find m∠3. Enter only a number.

Problem 2 Got It? ▱ MNPQ has vertices M(0, 1), N(-1, 4), P(2, 5), and Q(3, 2).
a. Is ▱ MNPQ a rectangle? Explain.

Problem 2 Got It? ▱ MNPQ has vertices M(0, 1), N(-1, 4), P(2, 5), and Q(3, 2).
b. Is ▱ MNPQ a square? Explain.

Problem 2 Got It? ▱ MNPQ has vertices M(0, 1), N(-1, 4), P(2, 5), and Q(3, 2).
a. Is ▱ MNPQ a rectangle? Explain.

Problem 2 Got It? ▱ MNPQ has vertices M(0, 1), N(-1, 4), P(2, 5), and Q(3, 2).
b. Is ▱ MNPQ a square? Explain.