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This 2 page Study Guide was uploaded by Mrs. Haley Hartmann on Monday October 5, 2015. The Study Guide belongs to MTH351 at Central Michigan University taught by Staff in Fall. Since its upload, it has received 38 views. For similar materials see /class/218898/mth351-central-michigan-university in Mathematics (M) at Central Michigan University.
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Date Created: 10/05/15
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 quotbuilding 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 151648 110247 and 1118248 It is assumed that you know how to use protractor to measure angles 131447 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 de nitions valid Explain 0 Parallel lines are lines that do not intersect 0 Angle is a union of two rays with a common point 0 Obtuse triangle is a triangle with an obtuse angle 0 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 quotTriangle Interior Angles Sum Theorem use your own words and prove it using the previous theorem AAT 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 Constructions 218224 Explain what Euclidean constructions are s paper folding a good example of Euclidean constructions Explain Carry out the following constructions using methods given in italics Do not forget a writeup on the test I ll ask you to carry out a construction and write up the steps Most of the following constructions are listed on my website where you can try them in Java Paper folding compass amp ruler Cabri o Midpoint o Perpendicular Bisector of a line segment 0 Angle Bisector o Perpendicular Line to a given line through a given point on or not on the given line 0 Parallel Line to a given line through a given point not on the given line Compass amp Ruler and Cabri o Transferring an Angle o Triangle given 3 sides 0 Equilateral Triangle o Triangle given 2 sides and incl angle 0 Triangle given 2 angles and incl side 0 Square given side 0 Square given diagonal 0 Regular Hexagon given side 0 Regular Hexagon given diagonal 0 Angle 60 30 120 75 45 without using protractor o constructions discussed on Thursday
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