Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Monthly Update sign up
Mailing List signup
Search
Follow The Annenberg Learner on LinkedIn Follow The Annenberg Learner on Facebook Follow Annenberg Learner on Twitter
MENU
Learning Math Home
Geometry Session 1, Part C: Folding Paper
 
Session 1 Part A Part B Part C Part D Homework
 
Glossary
Geometry Site Map
Session 1 Materials:
Notes
Solutions
Video

Session 1, Part C:
Folding Paper

In This Part: Constructions | Constructing Triangles | Concurrencies in Triangles
More Constructions

Problem C6

Solution  

Start with a square sheet of paper.

a. 

Construct a square with exactly one-fourth the area of your original square. How do you know that the new square has one-fourth the area of the original square?

b. 

Construct a square with exactly one half the area of your original square. How do you know that the new square has one half the area of the original square?

c. 

Construct a square with exactly three-fourths the area of your original square.


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Think about how you might construct the exact side lengths needed for these squares. For example, the first square will need a side length exactly one half the original. The third square is very difficult!   Close Tip

 

Problem C7

Solution  

Recall that the centroid is the center of mass of a geometric figure. How could you construct the centroid of a square?


Take it Further

Problem C8

Solution

When you noticed concurrencies in the folds, were you sure that the segments were concurrent? What would convince you that, for example, the medians of every triangle really are concurrent?


 

Next > Part D: Basic Objects

Learning Math Home | Geometry Home | Glossary | Map | ©

Session 1: Index | Notes | Solutions | Video

© Annenberg Foundation 2014. All rights reserved. Legal Policy