ࡱ> l` ybjbj 6thI^&&& 'ttt8 '>R (f< GCSc$8h-&fU L&fr1( &Vf 0Htp F0Vhc hVVh&jH)Ϥm^ ' ' 'DP$ ' ' 'P ' ' ' Chapter 1 Points, Lines, Planes and Angles  INCLUDEPICTURE "http://members.aol.com/frustum1/patterns.gif" \* MERGEFORMATINET  What you have done is 1) look for a pattern 2) made a conjecture 3) used logical reasoning to verify your conjecture That is what we do in geometry using definitions, postulates, properties and theorems to verify our conjectures. A. Undefined terms: points, lines, planes READ ABOUT THEM PG. 5 B. Definitions - State the meaning of a concept. Definintions are reversible. Definitions contain the least possible amount of information. C. Postulates or axioms are things we accept to be true. Not necessarily reversible. D. Theorems things we prove to be true 1.3 Segments, Rays and Distance  HYPERLINK "../../../SKETCHPAD%20FOR%20GEOMETRY/CH%201/1.3%20Segments,%20Rays,%20Distances%20,%20SAP2.gsp" SKETCHPAD Get into groups and find the following :  Ex 1) The ray opposite to  EMBED Equation.DSMT4  is _______ 2) The length of  EMBED Equation.DSMT4  is ________. 3) The distance between R and E is _______ 4) The midpoint of  EMBED Equation.DSMT4  is _____________ 5) The coordinate of midpoint of  EMBED Equation.DSMT4  is ___________ 6) Give me a rule for finding the coordinate of a midpoint _______________________________________________________________________ _______________________________________________________________________ 7) Give me a rule for finding the distance between 2 points _______________________________________________________________________ _______________________________________________________________________  8) You are told that segment AB, notation AB, is 10 cm, segment AC is 3 cm, how long is segment BC ? You might have to think about this a little. A picture would definitely help.  A. Segment Addition Postulate _____ _____ _____ If B is between A and C, then AB +BC = AC Draw a picture: Ex.. If AB = 6 andBC = 8, then AC = Ex. If AC = 12, AB = 15, BC = 3, which point is between the other two? Ex. If L is between P and Q, and PL = 6x-5, LQ = 2x + 3, and PQ = 30? What is x? 1.4 Angles Angle Addition Postulate _____ _____ _____ ( Used two ways) A. If point B lies in the interior of THEN statements. Complete the following and finish for homework if necessary. 1. If SYMBOL 208 \f "Symbol"1=90SYMBOL 176 \f "Symbol", then SYMBOL 208 \f "Symbol"1 is __________________________________________________. 2. If two angles have the same degree measure, then __________________________ 3. State the converse of #1 and #2 _________________________________________________________________ _________________________________________________________________ 4. Turn this statement into a conditional statement and then its converse. All right angles are congruent. ______________________________________________________________________ ________________________________________________________________________ 5. There are 2 pairs of postulates that are converses of each other regarding lines and points. Name them and explain what they say. 6. (a) Write the converse of the statement If point P is equidistant from the coordinate axes, then point P is on the line y = x. _________________________________________________________________________ (b) Give an example of a true statement whose converse is false. _________________________________________________________________________ (c) Give an example of a true statement whose converse is also true. _________________________________________________________________________ 7. In Algebra, you have learned so solve an equation by balancing while solving for x.  Give reasons, using your past or present text, for the following steps in solving the algebraic equation. 2-2 Proof Properties Memorize SOON!!!!! Properties of Equality Make file cards 1. ADDITION PROPERTY If a = b and c = d, then __________________________________________________ 2. SUBTRACTION PROP If a = b and c = d, then ___________________________________________________ 3. MULTIPLICATION PROP If a = b, and c exists, then ________________________________________________ 4. DIVISION PROP If a = b, and c  EMBED Equation.DSMT4  0, then _________________________________________________ 5. SUBSTITUTION If a = b, then either may replace the other in any equation. 6. REFLEXIVE a = a 7. SYMMETRIC PROP If a = b, then __________________________________________________________ 8. TRANSITIVE PROPNN If a = b, and b = c, then _________________________________________________ Properties of Congruence 1. REFLEXIVE PROP:  EMBED Equation.DSMT4  2. 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