Superlesson
Project 6-2
Foundations of Algebra and Geometry
Chapter 6, Using Ratios to Compare
You can use angles to analyze geometric relationships on paper or in the sky.
Part A, Angles and Angle Relationships
1. The figure shows that a pentagon can be formed from three triangles. The sum of the measures of the angles of the pentagon equals the sum of the measures of the angles of three triangles.
Sum of measures of angles of pentagon = 3 x 180° = 540°
a. Sketch each figure listed below. Find out the number of sides each has by looking it up in a Glossary. Then complete the table by drawing diagonals from a single vertex of each figure to the other vertices to create triangles.
Name of Polygon Number of Sides
Number of Triangles Formed
Sum of Measures of Angles Pentagon 5 3 3 x 180° = 540° Hexagon __ x 180° = ___ Heptagon __ x 180° = ___ Nonagon __ x 180° = ___ Dodecagon __ x 180° = ___ b. Describe the relationship between the number of sides and the number of triangles.
c. What is the sum of the measures of the angles of a polygon with 102 sides? Explain.
Part C, Blow It Up and Scale It Down
2. Use the Internet to answer the following questions.
a. The figure shows a scale model of the Earth and the moon. Find the radius of the moon (km) by writing a proportion involving the dimensions of the scale model and the known distance to the Moon.
b. For a science project, Pam decided to build a scale model of the solar system. She placed Earth 3 feet from the Sun. In her almanac she found that Pluto, the most distant planet, is 5,910,000,000 km from the Sun. How far should she place Pluto from the Sun? Find the distance from Earth to the Sun and use this information to write a proportion to find out how far Pluto should be from the Sun in the model.
c. What difficulty will Pam face in constructing her model?
Part E, Making Connections
3. A spy satellite is in orbit 987 km above Earth's surface. Points A and B are the most distant points on Earth that are visible to cameras aboard the satellite. Earth's radius is r.
a. Find distance OS, Earth's radius plus the satellite's height.
b. Use the Pythagorean Theorem to find distance AS.
c. Compare AS and OS. What isd. What fraction of the Earth's circumference is the satellite capable of spying on?
