Geometry 6-9 Proofs Using Coordinate Geometry

by Matthew Richardson

| 16 QuestionsNote 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.

1

10

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.

2

2

10

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)?

3

3

40

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

4

50

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

6

6

10

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

7

10

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?

(a, b)

(a, -b)

(-a, -b)

(-a, b)

8

9

10

8

5

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?

SSS

SAS

ASA

AAS

9

5

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

SSS

SAS

ASA

AAS

10

5

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

SSS

SAS

ASA

AAS

11

10

Review Algebra: Solve. Round to the nearest tenth if necessary.

Select all that apply.

x = 14

x = 12

x = 144

x = -12

12

10

Review Algebra: Solve. Round to the nearest tenth if necessary.

Select all that apply.

r = -8.1

r = -8

r = 8

r = 8.1

13

10

Review Algebra: Solve. Round to the nearest tenth if necessary.

Select all that apply.

k = -19.3

k = -16.6

k = 16.6

k = 19.3

14

10

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

15

10

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

16

10

Reflection: Math Success

Add to my formatives list

Formative uses cookies to allow us to better understand how the site is used. By continuing to use this site, you consent to the Terms of Service and Privacy Policy.