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Geometry Chapter 6 Review Classify each statement as true or false. 1) If a > b and c> d, then a + b > c + d. FALSE 2) If B is on AC, then AB + BC > AC. FALSE 3) If x > y and y> 0, then xy> 0 TRUE 4) If S is in the interior of PQR, then mPQR > mSQR TRUE Suppose you plan to write an indirect proof of the statement: If n > 10, then 2n + 3 > 23. Write the correct first sentence of the indirect proof. Assume temp. that 2n+3 < 23 Indirect Proof: Given: 5x + 5 = 25 Prove: x = 3 Assume temp that x = 3, then 5x + 5 = 5(3) + 5 = 20 But this contradicts the given that 5x + 5 = 25. Thus our assumption is false, Therefore x does not equal 3. Complete each statement by writing <, =, or >. < 1) If mF > mG, then FH H HG. 2 2) If m 3 > m4, then FH > 1 2 3 4 HG. F J 3) If FH < HG, then m1 > m2. G In rectangle RECT, the diagonals intersect at M, mRMT = 88, and mRME = 92. Which is longer, RE or RT? __________________________ RE In triangle RST, m1 > m R or T . > In triangle RST, if RT < RS, then mT In triangle RST, if mTSR < mR, then RT mTSR < ST. T 1 S R If RS = 15 and ST = 12, then the length of RT must be greater than and less than . 3;27 If m1 = 135 and mR = 60, then the longest side of triangle RST is _________________________________. RS Complete the statements by writing <,=, or >. B 15 E 12 40 42 14 1 2 58 A 60 1) AB < AC C D G 2) DG < F 12 > GF 3) m1 m2 What can you deduce? Name the theorem. F 18 G 88 E 92 18 EF>ED by SAS Ineq. Thm D t a 1 2 b Complete the indirect proof Given: Transversal t cuts lines a and b; a is not parallel to b Prove: 1 and 2 are not supplementary Proof Angles 1 and 2 are supp. Assume temporarily that 1) ________________________________. a//b. Then 2)_____________________ since if two lines are cut by a transversal and same-side interior angles are supplementary the lines are parallel. But this contradicts the given information that 3) a is not // to b. . Angles 1 and 2 are supp. Therefore the temporary assumption that 4) _______________________________ must be false. Angles 1 and 2 are not supp. Therefore 5) __________________________________________________________. Fill in the blanks. 24. Given: AB > CD Prove: AC > BD A Statements B C Reasons AB > CD GIVEN 1) BC = BC REFLEXIVE PROPERTY 2) AB + BC > BC + CD A PROPERTY OF INEQUALITY AB + BC = AC; BC + CD = BD 3) SEGMENT ADDITION POSTULATE AC > BD 4) SUBSTITUTION D HW • Chapter Review P.235 #1-18 Check your odd answers Look at Powerpoints to study