Google Earth Voyager Story: Triangular Structures
In this exploration, we will explore triangles by looking at different architectural sites. In particular we look at the Bank of China in Hong Kong and then the Eiffel Tower. Each building is an application of the geometric principles behind triangles. To see the Google Earth version of this lesson go to this link.
To see the complete collection of Google Earth Voyager Stories from Media4Math, go to this link.
1. Introduction to Triangles: The Bank of China Tower
To start this lesson, watch this video about the Bank of China in Hong Kong, which has lots of triangles built into its design.
2. The Geometry of the Eiffel Tower
Watch this video clip to learn about the Eiffel Tower, its architect, and how it uses triangular trusses.This segment introduces the concept of triangular shapes used in the structure of the Eiffel Tower.
In addition the following engineering concepts are introduced:
- Static Equilibrium
3. Constructing an Isosceles Triangle with the TI-Nspire
In this video construct an isosceles triangle using the TI-Nspire graphing calculator. All keystrokes are clearly shown for constructing this type of triangle.
The following geometric concepts are introduced:
- Perpendicular Bisector
- Line Segment
- End point
- Congruent Sides
4. The Rigidity of Triangles
In this video learn about the geometric properties of triangles that give them their rigidity. This geometric property is what makes triangles so effective for construction. This video is a continuation of the geometric construction using the TI-Nspire (see previous section).
The rigidity of triangles is contrasted with the flexibility of quadrilaterals. All triangles with the same side lengths are congruent. This isn't necessarily the case with quadrilaterals.
5. The Side-Side-Side Postulate
In this video learn about the Side-Side-Side Postulate: When two triangles have corresponding sides that are equal to each other, then the triangles are congruent. This means that not only are the corresponding side lengths congruent, but so are the corresponding angles.
6. Triangular Trusses
In this video learn about the structure of a triangular truss. In particular, we look at triangular trusses in the shape of an isosceles triangle. We also look at a version of a truss that has a vertical support that splits the isosceles triangle into two congruent right triangles. The perpendicular bisector of an isosceles triangular base is also an angle bisector.
7. Triangle Inequalities and Truss Size
In this video learn about the triangle inequality that involves the three sides of a triangle. We look at different sizes for trusses to discover the limitations on the size of a triangular truss. We go through the steps of building a triangular truss with a vertical support. We analyze the configuration of trusses into quadrilateral shapes and see how different forces create different areas of compression and tension.
9. Similar Triangles
In this video learn about similar triangles. For two similar triangles we look at the corresponding parts that are congruent and those that are proportional. We look at trusses that are made up of similar triangles.
10. Geometric Proof
In this video we go through a geometric proof to show that adjacent sets of triangular trusses on the Eiffel Tower are similar. The proof involves finding corresponding angles that are congruent.
We look at the Eiffel Tower's continuing importance to France and world culture.