Superlesson
Project 4-1

Superlesson
Project 4-2

Superlesson
Project 4-3

Geometry

Chapter 4, Triangles

If you take a close look at the frame of a bicycle, you will probably be able to identify triangular shapes within its structure. Many other structures also have triangles incorporated into their design because of the structural stability of this shape.

Part A, Isoceles Triangles

1. Examine the triangular shapes in the bicycle pictures.

a. Look at the bicycles shown on each of the two sites listed below. Identify the isoceles triangle(s) in each frame. Sketch the portion of each frame which contains the isoceles triangles. Indicate the congruent sides of each triangle.
Hint: Take a close look at the back wheel.

• Site #1: Exploratorium
  Look at the first bicycle drawing.
  
• Site #2: Brodie Bikes

b. In the two isoceles triangles that you have sketched, measure the angles opposite the congruent sides. What can you conclude about the angles opposite the congruent sides of an isoceles triangle?

 

Part D, Lines Associated With Triangles

2. Print out a copy of the mountain bike and racing bike shown at the sites below.

• Mountain Bike
  
• Racing Bike

a. Estimate the location of the center of gravity, or centroid, for the triangle which makes up the main part of the frame in each of the two bicycles.

b. How is the center of gravity different for the mountain bike and the racing bike?

c. How would this difference be important for the function of each of the bicycles?