Properties of Triangles II

Introduction

Dear Student,

Today you will be completing a WebQuest on MORE properties of triangles, PART II! How much do you know already? We will be starting this WebQuest in class and it is to be completed by the beginning of tomorrow's class. Good luck!

Best,

Miss Marquez

Task

You will work through the six websites and answer the questions related. You have the opportunity to complete most of the assignment in class so use your time wisely. If you are able to answer the questions without visiting the website, that is okay, but please visit the website before asking for help.

Good luck!

Process

7. Students will visit website 7:

                  a. Supplementary Angles are angles that ___________ to be ______________.

                  b. Drag the points around. Explore what happens.

                  c. When put together, what do supplementary angles make? Explain what that is..

8. Students will visit website 8:

  1. What are congruent triangles?
  2. What are the four rules we can use as “shortcuts for congruence?” Explain each.
  3. What is the additional rule for right triangles? Explain it.
  4. Why doesn’t AAA work as a congruence shortcut?
  5. Why doesn’t SSA work as a congruence shortcut?

 

9. Students will visit website 9:

How do you find the area of a triangle when:

  1. Given the base and the height?
  2. Given the length of 3 sides? (Heron’s Formula)
  3. Given Side, Angle, Side
  4. Given an equilateral triangle
  5. Given three vertices drawn on a grid.

Give an example of each.

 

10. Students will visit website 10

  1. What is the exterior angle theorem?
  2. Provide two example problems of how to use the exterior angle theorem.
  3. Provide a two-column proof of the exterior angle theorem.

 

11. Students will visit website 11

  1. What is the triangle inequality theorem?
  2. Write down the three inequalities given.
  3. What is the angle-side relationship?
  4. Copy down one of the examples given (either on the page or in the video) of the angle-side relationship.

 

12. Students will visit website 12.

  1. Complementary Angles are angles that _____________ to be ______________.
  2. Copy Down two of the Picture Examples of Complementary Angles, (either on the page or in the video).
  3. Copy Down two of the Word Problem Examples of Complementary Angles, (either on the page or in the video).

 

13. Students will visit website 13.

  1. What is the Distance Formula?
  2. What is the Midpoint Formula?
  3. The Distance Formula comes from which major theorem? Explain How?
  4. Copy Down one of the Examples of the Distance Formula, (from the video).
  5. Copy Down one of the Examples of the Midpoint Formula, (from the video).

 

14. Students will visit website 14.

  1. What is a Transversal?
  2. Alternate Interior Angles are ___________.
  3. Alternate Exterior Angles are ___________.
  4. Same Side Interior Angles are __________.
  5. Same Side Exterior Angles are __________.
  6. Corresponding Angles are ______________.
  7. Go to https://www.ixl.com/math/geometry/transversals-of-parallel-lines-find-angle-measures and work through the practice problems.

 

15. Students will visit website 15.

  1. What is a Median of a Triangle?
  2. How many Medians does a Triangle have?
  3. Drag all of the points around. Explore what happens.
  4. Name the 4 Properties of Medians.
  5. What is the Point where the Medians meet, called?

 

 Part 2: Choose two of the following three to complete. Your answers will be emailed to me:

16. Students will visit website 16

 

17. Students will visit website 17

 

18. Students will visit website 18

 

 Part 3:

19. Students will visit website 19

  1. What is an altitude of a triangle (in the sense that it is being used on that page)?
  2. What is the orthocenter of a triangle?
  3. When will the orthocenter be inside the triangle?
  4. When will it be outside the triangle?
  5. When will it be on the triangle?
  6. What are the steps to constructing the orthocenter of the triangle?

20. Students will visit website 20

  1. What is a median of a triangle?
  2. What is the centroid of a triangle?
  3. The centroid is always ___________ of the triangle.
  4. Each median divides the triangle into:__________________
  5. Each centroid is exactly ________________ of the way along the median.

Put another way, the centroid divides each median into: _______________________

Evaluation

CATEGORY

4

3

2

1

Mathematical Concepts

Explanation shows complete understanding of the mathematical concepts used to solve the problem(s).

Explanation shows substantial understanding of the mathematical concepts used to solve the problem(s).

Explanation shows some understanding of the mathematical concepts needed to solve the problem(s).

Explanation shows very limited understanding of the underlying concepts needed to solve the problem(s) OR is not written.

Google Quiz Score

Answered 6 or 7 out of 7 correctly.

Answered 5 out of 7 correctly.

Answered 4 out of 7 correctly.

Answered less than 3 out of 7 correctly.

Working and using time wisely in class

Student was an engaged learner who did not disrupt the work of others  and was working cooperatively throughout the webquest.

Student was an engaged learner but at times distracted others and/or did not working cooperatively during the entire webquest.

Student cooperated, but needed cues to stay on-task.

Student did not work effectively in class.

Mathematical Reasoning

Uses complex and refined mathematical reasoning.

Uses effective mathematical reasoning

Some evidence of mathematical reasoning.

Little evidence of mathematical reasoning.

 

Conclusion

You may have known some of these properties before, but you may not have known why.

1) Name one property you may have memorized before but that now you fully understand. 

2) Is there a property about triangles you would like some clarification on?

Credits

Work Cited

 

Rabber, Robert. “Coach Raber's Triangle WebQuest!” Create WebQuest, www.createwebquest.com/webquest/coach-rabers-triangle-webquest.