Saturday, July 13, 2013

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


  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.


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.