Geometry Module 6 DBA

Question:

Determine the type(s) of the triangle with the given coordinates.

X(6,1) Y(-2,-3) Z(0,3)

Answer:

XY = (6 − (− 2))

2

+ (1 − (− 3))

2

XY = (8)

2

+ (4)

2

XY = 64 + 16 = 70

YZ = (0 − (− 2))

2

+ (3 − (− 3))

2

YZ = (2)

2

+ (6)

2

YZ = (4) + (36) = 40

XZ = (6 − 0)

2

+ (1 − 3)

2

XZ = (6)

2

+ (− 2)

2

XZ = (36) + (− 4) = 32

According to the calculations the triangle is scalene

Do the points (0,0) (a,0) (a,a) and (0,a) represents a special quadrilateral? If so, which one?

If not, explain why not and what should be changed? Be sure to sketch the quadrilateral.

If it does represent a special quadrilateral, use the formulas from this module to prove one

of the properties from section 6.01a. Show and explain your work including a sketch.

A. B.

Draw a rectangle and one of its diagonals. Determine if the two triangles formed are

congruent. If they are congruent, prove using a two-column, flow or paragraph proof that the

diagonal divides the rectangle into two congruent triangles? If the two triangles are not

congruent, explain why not using mathematical language from modules 1 through 6.

Your response must be at least three paragraphs (1 paragraph per question).

This question required:

1. The course resources and your teacher says that note taking is really helpful in

mathematics. As you went through this module would you agree or disagree with that?

What additional advice would you give to a student that is beginning this part of the

course today?

Choose 2 of the following questions:

2. What new information have you learned from this module? What surprised you about

what you learned? What knowledge from your past courses did you use in this module?

3. Over the course of this module, what concept did you find the most challenging? What

did you do to clarify the concepts in this module to further your learning? How did I move

through roadblocks or challenges?

4. Briefly explain a concept in this module and give at least one real world example that

demonstrates the concept that you have selected. Share an original example that you

have written and solved. Be sure it is not given in the course content or in the

application question above.

5. What would you do differently in this part B of the course that you didn’t do in part A?

6. What was your favorite concept of this module and why? Would you like to learn more

about this concept?

Rubric

Not applicable Needs

Improvement

Proficient Exemplary

(0 points) (up to 5.5 points) (up to 8.5 points) (up to 10 points)

Part 1

Application

Solution is

incorrect and the

student did not

show or explain

work or work the

problem incorrectly.

Solution is

incorrect; however

the student showed

their work and

made an error(s)in

calculations. OR

Solution is correct

but there is no

work shown or

explained

Solution is correct,

however there is

little work shown

for the problem.

Solution is correct.

All work shown and

explained using

mathematical

language from this

module.

Part 2

Find the

Error

Errors not found or

explained. Error in

attempt to rework

the problem.

Some or no errors

found. Problem

reworked out

partially.

All or most errors

found and

explained.

Problem not

reworked correctly.

All errors found

and explained.

Problem worked

out correctly with

all work shown

Part 3

Discussion

Question

Discussion

question not

answered or

discussed without

correct conclusion

Errors in

discussion. Little to

no mathematical

language included

in the discussion

Discussion has few

errors. Little to no

mathematical

language included

in the discussion

Discussion is

correct using

mathematical

language included

in this module to

answer the

discussion

question.

Part 4

Reflection

Reflection not

answered.

Reflection

attempted but

response is less

than 3 paragraphs.

No specific

examples given.

3 paragraphs are

written but less

than 2 sentences

and/or meaningful

discussion is

missing for a

paragraph. Little to

no specific

examples given.

3 paragraphs of at

least 3 meaningful

sentences each

answering each

question reflecting

on this module.

Specific examples

are given to justify

the reflection

questions.