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Alternate Interior Angle Theorem By: Miguel Reyes Whats a Alternate Interior Angle Theorem? • If two parallel lines are cut by a transversal, the alternate interior angles are congruent. Example The End Complementary and Supplementary angles By Ryan Herlihy QuickTime™ and a decompressor are needed to see this picture. Complementary angles • These are 2 angles that add up to 90º • It is 2 adjacent angles or 2 non adjacent angles adding up to 90º Practice Problems QuickTime™ and a decompressor are needed to see this picture. +5 Ex:Find x QuickTime™ and a decompressor are needed to see this picture. Since this is a complementary angle it equals 90º This means that: x+5+45=90º -50 -50 x = 40º Supplementary angles – All supplementary angles are 2 angles that add up to 180º – It can be adjacent or non adjacent angles adding up to 180º QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. ________________Practice Problems_________________ • Find x if <1 and <2 are supplementary <1 = 57º <2 = x+33 57+x+33=180 -90 -90 X = 90º • QuickTime™ and a decompressor are needed to see this picture. X+25 Find x. if line wx is supplementary X+25+60=180 -85 -85 x = 95 Helpful links • http://www.mathleague.com/help/geome try/angles.htm http://www.mathwarehouse.com/geometry/angle/su pplementary-angles.php http://www.aaaknow.com/geo-comp-or-sup.htm Corresponding Angles Postulate When two parallel lines are cut by a transversal, the resulting corresponding angles are congruent Properties • Any angles that are corresponding to each other are congruent Example Problems • • • • 1. What angle is angle 1 congruent to? 2. What angle is congruent to angle 6? 3. Are angle 2 and 4 congruent? 4. What angle is congruent to angle 7? • • • • • Answers: 1. Angle 3 2. Angle 8 3. Yes 4. Angle 5 Web Links • http://hotmath.com/hotmath_help/topics/corre sponding-angles-postulate.html • http://www.mathwarehouse.com/geometry/an gle/transveral-and-angles.php • http://en.wikibooks.org/wiki/Geometry/Postula tes_%26_Definitions Segment Addition Postulate • If a segment is divided into two smaller segments, the sum of the mini two must equal the length of the whole segment. Rules, Properties, and Formulas • If A, B and C are collinear, and B is between A and C, then AB + BC = AC. Examples • Point L is between points N and M. If NL= 6x-5, LM= 2x+3, and NM = 30, find x, NL, and LM Answer: x=4 • Point W is between R and S. If RS = 7x+8, RW = 4x3, and WS = 6x+2, find x, RW, WS, and RS. Answer: x= 3 • B is between A and C. Find the value of x and the measure of BC if: AB = 3, BC = 4x + 1, AC = 8. Answer: x=1 Web Links • http://www.gradeamathhelp.com/segme nt-addition-postulate.html • http://www.coursenotes.org/Geometry/Segments_and_Ra ys/Segment_Addition_Postulate • http://www.tutorvista.com/math/segment -addition-postulate-definition Law of Syllogism The Law of Syllogism is used when writing a deductive statement. It states: A = B B = C A = C My goal is to help jog your memory about the Law and how to use it. Steps to create: • Step 1: create a simple if-then statement. • Step 2: Use the then portion as the new if and relate that to something else. • Step 3: Use the first if portion and relate that to the final then. Examples on Next Slide Examples: • If it is snowing, then it is cold out. If it is cold out then it is Winter. If it is snowing, then it is Winter. • If the weather is fine, then school is open. If school is open, kids will go to school. If the weather is fine, kids will go to school. • If the Jets beat the Steelers, then they will advance. If they advance, they will go to the Super Bowl. If the Jets beat the Steelers, they will go to the Super Bowl. http://www.freelawanswer.com/law/31713-freelawanswer.html