Geometry: Special Segment Construction with Paper Folding

Pg 5. Special Segment Construction

After the paper triangle folding lesson, I gave students this assignment. This turned out really well. Students cut out their own triangle and when they came across significant scenarios - same altitude, median, etc. we got to discuss this one on one.

 

Here's an example of an obtuse isosceles triangle I was assigned in a workshop.

 

Pg 6. Venn Diagrams of Triangle Relationships

I noticed that some of my students could use a visual diagram for equilateral and equiangular as a subcategory of isosceles and acute.

Pg 7. Intersection of Medians

Pg 8. Intersection of Altitudes

Pg 9. Intersection of Perpendicular Bisectors

Pg 10. Intersection of Angle Bisectors

Pg 11. Constructing Altitudes

 

Pg. 12 Midsegments

Steps:

1. Cut a triangle out.
2. Fold and pinch each side side in half to locate the midpoint.
3. Fold a vertex to the midpoint of the opposite side and crease the midsegment.
4. Using a straight edge either trace the fold or connect the midpoints using a straight line. There should be three midsegments.
5. (EXTENSION) Cut along the midsegments to divide the original triangle into four congruent triangles similar to the original.

OR

My first year, I had students cut out a triangle and then duplicate three more congruent triangles by tracing/copying the original.

I then had the students trace them on a piece of paper.

After tracing, students measured all of the segments and angles. We then compared the lengths using ratios. This showed an approximate scale factor of 2. We also compared and showed the angles of simlar figures to be congruent.

 

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Geometry: Midpoint Formula and Distance Formula

Pg 5. Discovering Midpoint Formula

 

Pg 6. Midpoint Formula

 

Pg 7. Midpoint Formula: Working It Backwards

 

Pg 8. Where does the Distance Formula Come From?

 

Pg 9. Distance Formula

 

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Geometry: Types of Lines and Relationships

Pg. 7. Lines, Line Segments, and Rules

Original Foldable: Pocket Book

This foldable takes a looooonnnnggg time to complete. I suggest finding another strategy. Suggestions?

QUICK CHECK FOR UNDERSTANDINGS: Book foldables may be time consuming, but they can be reusable. I had my students pull out all cards from the books, mix them up, and match them back to the correct pocket. It is easier to have them compare to a neighbor and monitor their results closely. I really like the disscussions that arise from who's right and wrong.

QUICK AND EASY: 'Types of Lines' foldable:

Line

Segment

 

Ray

Perpendicular

Haven't figured out how to work parallel into this.

This is one of my favorites. I had a student struggling with this concept at Sylvan. We created this foldable in under two minutes, had a one to two minute reteach, and she mastered the concept. She still has this in her folder and enjoys teaching other students that struggle.

This is paired with another trifold foldable in my journal.

 

Pg. 8. Relationships of Segments and Distance

 

Pg. 9. Segment Bisector (this is a trifold)

 

 

 

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