I-MATH

Similar Triangles

Similar triangles are one of the most useful topics in geometry, in terms of applications to "real life"! Similarity is a concept that is the basis of scale drawing in architecture and engineering, used in building scale models from toy model airplanes to scale models in industry and architecture, and is very useful in measuring the heights of inaccessible objects. This type of measurement is useful for finding the heights of inaccessible buildings and mountains, and even distances in navigation.

Architects use scale drawing to design houses, hotels, and all types of projects. The following floor plan is an example of a simple house design, originally drawn at the scale 1/4" = 1'-0".This drawing is "similar" to the actual floor plan of the house: every 1/4" on the drawing would represent 1 foot in the actual house when it is built. The drawing below is reduced to fit on this web page. Scale drawings like this are essential in all aspects of architectural design and in the construction business, as well as in many other design fields, from airplane design to the design of everything from toys to cities.

The floor plan above came from a fascinating and comprehensive website on architecture, which is worth exploring beginning at the following link.This website has hundreds of links to websites on architecture:

http://architecture.about.com/arts/architecture/msubmenu4.htm

The beautiful scale drawing below of a home in Mauna Lani, Hawaii. was designed and drawn by an architectural firm called Architects Studio, whose offices are in Santa Barbara, California.

 

As you may recall, Connections and Applications of mathematics is one of the new NCTM Standards, as stated in the Introduction to I-MATH. The projects in this chapter relate directly to this Standard.

My students use similar triangles to measure the height of a tree or building in their neighborhood, and my students at my high school use the same method to measure the height of a coconut tree on campus. Click on the link below to visit the Creative Geometry website, and learn more about this project.

http://mathforum.org/~sanders/creativegeometry/4.1geometrees.htm

Go on to The Conics

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