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MTH 351 Test 1 Study Guide
Deductive System of Geometry
In general, good notes taken in the class should do; for an extended review you may consult
the book (pages are given in parentheses).
Explain why Eratosthenes’ method of calculating the Earth’s circumference works. Apply it to
find the circumference. (240, 247)
Who is Euclid and what is he famous for? (31)
Explain how the system of geometry is built. What are its “building blocks”? Which “blocks”
provide Geometry with the vocabulary and which ones provide principles? (38, 39)
Which are the undefined terms in Euclidean geometry? How do they differ from definitions?
Review the angles vocabulary and definitions (44, 242). Solve related problems: #15-16/48;
#1-10/247 and #11-18/248
It is assumed that you know how to use protractor to measure angles (#13-14/47)
Review the definitions we had (definitions in the book might be a bit different from those we
had in class): Parallel lines (55), Ray (41), Line Segment (41), Angle (42), Angle bisector (209).
I will not ask you to define these terms but rather to assess validity of a given definition:
Examples: Are these definitions valid? Explain.
• Parallel lines are lines that do not intersect.
• Angle is a union of two rays with a common point.
• Obtuse triangle is a triangle with an obtuse angle.
• Acute triangle is a triangle with an acute angle. Etc.
What is a postulate?
On how many postulates did Euclid build his Geometry?
Which is Euclid’s most influential postulate? What’s the story about it? (237).
What is a theorem?
Prove Vertical Angles Theorem (pg. 190)
Prove Alternate Interior Angles Theorem (notes).
We did not discuss the following two theorems in class. They are easy to prove, try to prove
them yourself before asking for help.
State the “Triangle Interior Angles Sum” Theorem {use
your own words) and prove it using the previous theorem
(AIAT) and the picture on the right.
Prove: If two lines a, b are parallel and line c is
perpendicular to a, then c is perpendicular also to b. (Use
one of the theorems above or another about angles
formed by two parallel lines cut by a transversal).
