Superlesson
Project 7-2
Geometry
Chapter 7, Similarity
Similar triangles occur quite frequently in architecture, even in the pyramids of early Egypt. The Great Pyramid in Ghiza was built somewhere between 2,000 and 3,000 BC and is the most comprehensively surveyed building in the world. Below, you will use your knowledge of similar triangles to calculate dimensions of the Great Pyramid.
Go to the Ghiza Web site to see a picture of the pyramids of Ghiza. The middle one in the row of the three large pyramids is the Great Pyramid. If you look closely, there appears to be a smaller pyramid taken off the top of the Great Pyramid. This smaller missing pyramid is called the capstone. Below is a simplified sketch of the Great Pyramid.
Part A, Similar Triangles
1. Use the Ghiza Web site to answer the following questions.
a. Assuming that the base of the pyramid is parallel to the base of the capstone, how do you know that
b. Go to the Hall of Records Web site to get data about the Great Pyramid. Go to 18:310 to findthe "edge to base" angle. Round this angle off to the nearest degree.
Part C, Dilations
2. Study the capstone of the Great Pyramid.
a. Some archaeologists believe that the Great Pyramid is a dilation of its capstone. Look at 4:22 to find the scale factor for this dilation.
b. Look at 11:151 to find the length of one base edge of the Great Pyramid. (Note that "PI" stands for "Pyramid Inch" and is a unit of measure just a bit longer than our current inch.)
c. Use your answer from 2b to find the length of the corresponding edge of the capstone. Does your answer roughly agree with the information given in 4:11? (Note that one cubit is 25 pyramid inches.)
d. Go to 0:1 to find the length of, a corner edge.
e. Use this to find the length of,a corner edge of the capstone.