Geometry Chapter 6 Review

Classify each statement as true or false. If a > b and c> d, then a + b > c + d.  If B is on AC, then AB + BC > AC.  FALSE FALSE If x > y and y> 0, then xy> 0 4) If S is in the interior of PQR, then mPQR > mSQR TRUE 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 mF > mG, then FH HG.  2) If m 3 > m4, then FH HG.  < 2 1 2 3 4 F G J H > > 3) If FH < HG, then m1 m2.

In rectangle RECT, the diagonals intersect at M, mRMT = 88, and mRME = 92. Which is longer, RE or RT? __________________________ RE

In triangle RST, m1 > m . R or T In triangle RST, m1 > m .  In triangle RST, if RT < RS, then mT mTSR  In triangle RST, if mTSR < mR, then RT ST.  > < T 1 S R If RS = 15 and ST = 12, then the length of RT must be greater than and less than . If m1 = 135 and mR = 60, then the longest side of triangle RST is _________________________________. 3;27 RS

Complete the statements by writing <,=, or >. 60 58 E 40 42 F G D 15 14 12 1 2 12 < > < 1) AB AC 2) DG GF 3) m1 m2

What can you deduce? Name the theorem. F E D 18 G 88 92 18 EF>ED by SAS Ineq. Thm

Angles 1 and 2 are supp. a//b. a is not // to b. Complete the indirect proof Prove: 1 and 2 are not supplementary Proof Assume temporarily that 1) ________________________________. 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) .   Therefore the temporary assumption that 4) _______________________________ must be false. Therefore 5) __________________________________________________________. Given: Transversal t cuts lines a and b; a is not parallel to b Angles 1 and 2 are supp. a//b. a is not // to b. Angles 1 and 2 are supp. Angles 1 and 2 are not supp.

Fill in the blanks. 24. Given: AB > CD Prove: AC > BD A B C D Statements 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

HW Chapter Review P.235 #1-18 Check your odd answers Look at Powerpoints to study