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Unformatted text preview: ; 0 (B) xy < 0 (C) x – y > 0 (D) x + y < 0 (E) x = y 2. 8. 3. 9. 4. 10. If x < 0 and y > 0, which of the following will always be greater than 0? (A) x + y (B) x – y (C) (D) (E)
x y 5. xy –2x 6. www.petersons.com Inequalities 235 2. GEOMETRIC INEQUALITIES
In working with geometric inequalities, certain postulates and theorems should be reviewed. A. If unequal quantities are added to unequal quantities of the same order, the sums are unequal in the same order. If AB > AE and (+ ) BC > ED then AC > AD B. If equal quantities are added to unequal quantities, the sums are unequal in the same order. AB > AE and (+ ) BC = ED then AC > AD C. If equal quantities are subtracted from unequal quantities, the differences are unequal in the same order. If AC > AD and (− ) BC = ED then AB > AE D. If unequal quantities are subtracted from equal quantities, the results are unequal in the opposite order.
AB = AC (− ) AD < AE DB > EC E. Doubles of unequals are unequal in the same order.
M is the midpoint of AB N is the midpoint of CD AM > CN Therefore, AB > CD www.petersons.com 236 Chapter 14 F. Halves of unequals are unequal in the same order.
∠ABC > ∠DEF
BG bisects ∠ABC EH bisects ∠DEF Therefore, ∠1 > ∠2 G. If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third. If ∠A > ∠B and ∠B > ∠C, then ∠A > ∠C. H. The sum of two sides of a triangle must be greater than the third side. AB + BC > AC I. If two sides of a triangle are unequal, the angles opposite are unequal, with the larger angle opposite the larger side. If AB > AC, then ∠C > ∠B. J. If two angles of a triangle are unequal, the sides opposite these angles are unequal, with the larger side opposite the larger angle. If ∠C > ∠B, then AB > AC. www.petersons.com Inequalities 237 K. An exterior angle of a triangle is greater than either re...
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- Spring '10