Geometry 6-9 Complete Lesson: Proofs Using Coordinate Geometry

By Matthew Richardson

Last updated over 3 years ago

16 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.

Solve It! The coordinates of three vertices of a rectangle are (-2a, 0), (2a, 0), and (2a, 2b). A diagonal joins one of these points with the fourth vertex. What are the coordinates of the midpoint of the diagonal? Justify your answer.

Problem 1 Got It? What is the advantage of using coordinates O(0, 0), E(0, 2b), and F(2a, 0) rather than O(0, 0), E(0, b), and F(a, 0)?

Geometry 6-9 Complete Lesson: Proofs Using Coordinate Geometry

Solve It! The coordinates of three vertices of a rectangle are (-2a, 0), (2a, 0), and (2a, 2b). A diagonal joins one of these points with the fourth vertex. What are the coordinates of the midpoint of the diagonal? Justify your answer.

Problem 1 Got It? What is the advantage of using coordinates O(0, 0), E(0, 2b), and F(2a, 0) rather than O(0, 0), E(0, b), and F(a, 0)?

Problem 2 Got It? Write a coordinate proof of the Triangle Midsegment Theorem (Theorem 5-1).

Coordinate Proof: Use coordinate geometry to prove that the diagonals of a rectangle are congruent.

Error Analysis: Your classmate places a trapezoid on the coordinate plane. What is the error?

Review Lesson 6-8: A rectangle ABCD is centered at the origin with A(-a, b). Without using any new variables, what are the coordinates of point C?

Review Lessons 4-2, 4-3, and 4-4: Which theorem or postulate would you use, along with corresponding parts of congruent triangles (CPCTC), to prove the congruence?

Review Lessons 4-2, 4-3, and 4-4: Which theorem or postulate would you use, along with CPCTC, to prove the congruence?

Review Lessons 4-2, 4-3, and 4-4: Which theorem or postulate would you use, along with CPCTC, to prove the congruence?

Review Algebra: Solve. Round to the nearest tenth if necessary.
Select all that apply.

Review Algebra: Solve. Round to the nearest tenth if necessary.
Select all that apply.

Review Algebra: Solve. Round to the nearest tenth if necessary.
Select all that apply.

Vocabulary Review: Follow the instructions to complete the items on the canvas.

Vocabulary Review: Follow the instructions to complete the items on the canvas.

Reflection: Math Success

Geometry 6-9 Complete Lesson: Proofs Using Coordinate Geometry

Solve It! The coordinates of three vertices of a rectangle are (-2a, 0), (2a, 0), and (2a, 2b). A diagonal joins one of these points with the fourth vertex. What are the coordinates of the midpoint of the diagonal? Justify your answer.

Problem 1 Got It? What is the advantage of using coordinates O(0, 0), E(0, 2b), and F(2a, 0) rather than O(0, 0), E(0, b), and F(a, 0)?

Problem 2 Got It? Write a coordinate proof of the Triangle Midsegment Theorem (Theorem 5-1).

Coordinate Proof: Use coordinate geometry to prove that the diagonals of a rectangle are congruent.

Error Analysis: Your classmate places a trapezoid on the coordinate plane. What is the error?

Review Lesson 6-8: A rectangle ABCD is centered at the origin with A(-a, b). Without using any new variables, what are the coordinates of point C?

Review Lessons 4-2, 4-3, and 4-4: Which theorem or postulate would you use, along with corresponding parts of congruent triangles (CPCTC), to prove the congruence?

Review Lessons 4-2, 4-3, and 4-4: Which theorem or postulate would you use, along with CPCTC, to prove the congruence?

Review Lessons 4-2, 4-3, and 4-4: Which theorem or postulate would you use, along with CPCTC, to prove the congruence?

Review Algebra: Solve. Round to the nearest tenth if necessary. Select all that apply.

Review Algebra: Solve. Round to the nearest tenth if necessary. Select all that apply.

Review Algebra: Solve. Round to the nearest tenth if necessary. Select all that apply.

Vocabulary Review: Follow the instructions to complete the items on the canvas.

Vocabulary Review: Follow the instructions to complete the items on the canvas.

Reflection: Math Success

Review Algebra: Solve. Round to the nearest tenth if necessary.
Select all that apply.

Review Algebra: Solve. Round to the nearest tenth if necessary.
Select all that apply.

Review Algebra: Solve. Round to the nearest tenth if necessary.
Select all that apply.