Math Giraffe
  • Start Here
  • Blog
  • Doodle Notes
  • Shop
  • Classroom Management & Ideas
  • Algebra
  • Geometry
  • Middle School
  • Inquiry Learning
  • Subscribe
  • About
  • Pre Algebra Doodle NoteBook
  • Finance Doodle NoteBook
  • Distance Math Activities
  • Start Here
  • Blog
  • Doodle Notes
  • Shop
  • Classroom Management & Ideas
  • Algebra
  • Geometry
  • Middle School
  • Inquiry Learning
  • Subscribe
  • About
  • Pre Algebra Doodle NoteBook
  • Finance Doodle NoteBook
  • Distance Math Activities
Search by typing & pressing enter

YOUR CART

Picture

12/3/2014 2 Comments

Discovery: Impossible Triangles

Guided Inquiry - Discovering Triangle Sum Theorem and Impossible Triangles
Pin it
This is such a fun way to introduce Triangle Sum Theorem.  This lesson is meant to be inserted right after reviewing the types of angles and triangle classifications (acute, obtuse, right, isosceles, equilateral, scalene).

Setup (Behind the Scenes)

Start by downloading a Geometry Software program (You can do this for free!)

Draw a quick triangle using the software and display each side length and angle measure.  These will adjust as a vertex is dragged.   Here are shots to show you how it looks in GeoGebra.  The triangle/shape button is first, then use the angle measure button to mark off the three points that name each angle.  (Do 3 times to get all 3 angles marked.)

Discovering Triangle Sum Theorem and Impossible Triangles - Hands-On Investigation
Hands-On Discovery - Triangle Sum Theorem and Impossible Triangles
Pin it
That's it for setup!  Once you get the hang of it, setting up an easy hands-on virtual discovery with GeoGebra only takes a minute.

The Lesson - Phase 1:

I set the stage as if we are just going over the triangle classifications we just reviewed.  I let one student at a time come up to manipulate the triangle. This works great on a smartboard or with a computer and projector.

 Ask the first student to drag a vertex to make the triangle a right triangle. He or she will drag a vertex and move things around until they can get one angle measure to be 90 degrees.  Success!  Then have another student come up.  The kids love this, and are so excited to play with the geometry software for the first time.

Calling up one student at a time, have them create a few basic types of triangles (something like an acute isosceles triangle, and then an obtuse isosceles triangle, and then even a right isosceles triangle).

Once you have been through a few of these successfully, give the next student a challenge to create a "right equilateral" triangle.  Do not hint that it cannot be done. Some students may figure out that it is impossible after just a minute and giggle as the student tries dragging a vertex different ways. 

Eventually, you can allow them to explain why they think the student at the board should give up. Continue on with some possible and some impossible triangles.

Request the following triangles:
  • right isosceles
  • obtuse scalene
  • obtuse equilateral
  • right obtuse
  • etc....

This leads to really great discussions. As an extension, you can have students list as many impossible triangles as they can.  Let your class explore and investigate triangles using the software.  Allow students to explain WHY certain triangles are impossible.

The Lesson - Phase 2:

Ask students to write a theorem stating what they discovered.

Try other hands-on activities exploring triangle sum theorem.  One option is to have students draw a large triangle, rip off all three vertices, and line them up in a row.
Discovering Triangle Sum Theorem - Guided Inquiry Lesson
Pin it
You can also have students use a protractor to measure the angles.  Allow them to work in pairs to write an official theorem.

Join together as a whole class to discuss and make sure that all pairs understand.
Picture
Pin it
Click here for the lesson pack of worksheets that I use to accompany this lesson.  There are materials for writing up the theorem, directions for cutting up a triangle, warm-ups, practice, and more.

Next Lesson:

Once your students have a good grasp of Triangle Sum Theorem, and get in some practice, move on to Triangle Inequality Theorem.  I start this one out by asking them to move the desks into a certain arrangement (that turns out to be impossible once they try to line them up!)  Read about structuring that lesson here.

To read more and get freebies and updates, subscribe to the Math Giraffe email list.  Just enter your email in the sidebar.

To Read Next:

2 Comments
LizOra
8/11/2017 10:26:26 pm

Bless you, dear woman! I'm so grateful I found you through TpT. I just bought the high school geometry bundle. Now these fabulous "rules" and routines. Just what my doctor ordered given 30+ years teaching and 72 years wise. I'm the 4th generation of teachers; sorta like being from a circus acrobat family. It's amazing what my sister and I learned from grandmother, great aunts, our mother, and each other. OHHHH how I wish my sister could have seen your Doodle Notes. She'd have been over the moon, just like I am.

Reply
Math Giraffe link
8/12/2017 06:08:04 pm

Aw, Liz,
Thank you so much!
This is wonderful to hear that you are enjoying the ideas.
I really appreciate you letting me know!
Teaching families are the best! :)
Thanks a ton for your kind comment. Have a wonderful weekend,
-Brigid

Reply



Leave a Reply.


    Archives

    November 2022
    October 2022
    September 2022
    August 2022
    March 2022
    December 2021
    November 2021
    September 2021
    July 2021
    April 2021
    November 2020
    September 2020
    August 2020
    April 2020
    March 2020
    November 2019
    September 2019
    April 2019
    March 2019
    February 2019
    January 2019
    November 2018
    October 2018
    September 2018
    August 2018
    July 2018
    June 2018
    May 2018
    April 2018
    March 2018
    February 2018
    January 2018
    December 2017
    November 2017
    October 2017
    September 2017
    August 2017
    June 2017
    May 2017
    April 2017
    March 2017
    February 2017
    January 2017
    December 2016
    November 2016
    October 2016
    September 2016
    August 2016
    July 2016
    June 2016
    April 2016
    March 2016
    February 2016
    January 2016
    December 2015
    November 2015
    October 2015
    September 2015
    August 2015
    July 2015
    June 2015
    May 2015
    April 2015
    March 2015
    February 2015
    January 2015
    December 2014
    November 2014


    RSS Feed

    Related Posts Plugin for WordPress, Blogger...
    Click to set custom HTML
Proudly powered by Weebly
Photos used under Creative Commons from kellywritershouse, Robert-Herschede, University of the Fraser Valley, mrhayata, Iwan Gabovitch, nateOne, Franklin Park Library, rhymeswithsausage, US Department of Education, Edsel L, Larry1732, philwarren, peteselfchoose, Dean Hochman, BryonLippincott, AFS-USA Intercultural Programs, Nilsze, philosophygeek, VividImageInc, cantanima, dcysurfer / Dave Young