Rest of Geom Chapter1 Part5

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Last example and the last section called "The If...Then...Sentence Structure. "Consider the Statement, "If I graduate from high school with an average greater than 90, then my parents will buy me a car." Will the student receive a car as a graduation present? The statement in the "If" clause identifies the 'condition' that must be met in order for the student to get the car as a present, while the statement in the "then" clause gives the consequence. Theorems in geometry are usually expressed as conditional statements in "If...then..." form." "'After' a theorem is proved, the "then" clause represents the fact that you are allowed to apply whenever the condition in the "If" clause is true. A theorem given in a later chapter is "If a figure is a rectangle, then its diagonals have the same length." After this theorem has been proved, you can use the fact that its diagonals have the same length whenever that property of rectangles is needed. 'Before' a proposed theorem is proved, the "if" clause contains what we know and the "then" clause identifies what we need to prove. A theorem that will be proved in a later chapter is" "If two sides of a triangle are equal in length," }"Given" " then the angels opposite them are equal." }"To prove" "Here is one possible format that can be used when beginning a proof." (Showing a perfectly even triangle meaning all sides are equal with point A as the 'vertex', point B, and point C all connected,) "Given: AB=CB Prove: Angle A = Angle C PROOF: Statements Reasons 1. AB=CB 1. Given (For all answers) 2. 2.______ Undefined terms and previously 3. 3.______ established definition, postulates, 4. 4.______ and theorems may be entered. Once this proof is complete, the theorem is taken as fact and can then be used to prove other theorems." (Now these all make common sense and look logical, better than the made of story of the Martians.) The exercises will now be on another day which is supposed to be a Friday. Normally Grandma will place a Geometry chapter on Tuesdays with Chemistry on Mondays, Algebra 1 on Wednesdays, and Algebra 2 on Thursdays. Given: