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 pts

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 pts

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 pts

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

4

50 pts

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

6

6

10 pts

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

7

10 pts

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 pts

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 pts

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 pts

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 pts

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

Select all that apply.

x = 14

x = 12

x = 144

x = -12

12

10 pts

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 pts

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 pts

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

15

10 pts

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

16

10 pts

Reflection: Math Success

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