Welcome to similarity Headquarters, division Triangles!
In this webpage, you will explore and discover the different similarity conditions that hold for triangles.
I wanted to create a webpage dedicated to triangle similarity, because of previous experience I had at the beginning of this semester. I was fortunate to receive an internship for math teaching, and our first unit was on triangle congruency and similarity. Some of the eTools our curriculum suggested weren't working too well, and I told my co-teacher that I would try to create a better applet since I was taking this class at the time. And thus, this webpage was born!
Historical Development and Background
Euclid is considered the father of geometry. As a well-known Greek mathematician, he lived during a time where great discoveries were being made in the math and sciences. He established the first school of mathematics in Alexandria. He compiled all of his findings in geometry in "The Elements," a 13-volume work which has often been used as the go-to text book in learning geometry.
As geometry is based off of a basic set of definitions and axioms, the framework of geometry is completely coherent in its conjectures and theorems.
Explanation of Mathematics
SIMILAR TRIANGLES
We say that triangle ABC and triangle DEF are SIMILAR if their corresponding angles are equal, and the corresponding sides are proportional.
Within a similar triangle, cool properties happen because of similarity and congruency conditions.
One of these properties is the SIDE SPLITTER THEOREM.
In this original GeoGebra applet, you'll be able to see how Side Splitter Theorem works. This is a neat theorem that results from triangle similarity.
Students are able to move points A, B, and C to shape whatever size triangle they would like.
They can also move point D to create whatever ratio they'd like between AD and DB.
Significance and Applications
Congruency and similarity have great applications in architectural and engineering constructs.
Epcot Ball, Walt Disney World in Orlando, FL.
The Bow Skyscraper, Foster + Partners in Calgary, Canada.
In terms of art, using congruent and similar images can produce beautiful artwork.
triangles + walls, 2003, Mark Robertson.
Euclid is considered the father of geometry. As a well-known Greek mathematician, he lived during a time where great discoveries were being made in the math and sciences. He established the first school of mathematics in Alexandria. He compiled all of his findings in geometry in "The Elements," a 13-volume work which has often been used as the go-to text book in learning geometry.
