In Exercises 1–12 classify each statement as true or false. A 1. If point A lies on BC, but not on BC, then B is between A and C. 2. A true conditional always has a true converse. 3. The statement "If ac = b, and c. bc, then a = b' is true for all real numbers a, 4. If two parallel lines are cut by transversal t and t is perpendicular to one of the lines, then t must also be perpendicular to the other line. 5. If AABC = ADEF and LA = LB, then DE = EF. 6. If the opposite sides of a quadrilateral are congruent and the diagonals are perpendicular, then the quadrilateral must be a square. JF GB 7. If A GBS ~ AJFK, then JK GS 8. The length of the altitude to the hypotenuse of a right triangle is always the geometric mean.between the lengths of the legs. 9. In any right triangle, the sine of one acute angle is equal to the cosine of the other acute angle. 10. If an angle inscribed in a circle intercepts a major arc, then the measure of the angle must be between 180 and 360. 11. The angle bisectors of an obtuse triangle intersect at a point that is equidistant from the three vertices. 12. If JK = 10, then the locus of points in space that are 4 units from J and 5 units from K is a circle.

In Exercises 1–12 classify each statement as true or false. A 1. If point A lies on BC, but not on BC, then B is between A and C. 2. A true conditional always has a true converse. 3. The statement "If ac = b, and c. bc, then a = b' is true for all real numbers a, 4. If two parallel lines are cut by transversal t and t is perpendicular to one of the lines, then t must also be perpendicular to the other line. 5. If AABC = ADEF and LA = LB, then DE = EF. 6. If the opposite sides of a quadrilateral are congruent and the diagonals are perpendicular, then the quadrilateral must be a square. JF GB 7. If A GBS ~ AJFK, then JK GS 8. The length of the altitude to the hypotenuse of a right triangle is always the geometric mean.between the lengths of the legs. 9. In any right triangle, the sine of one acute angle is equal to the cosine of the other acute angle. 10. If an angle inscribed in a circle intercepts a major arc, then the measure of the angle must be between 180 and 360. 11. The angle bisectors of an obtuse triangle intersect at a point that is equidistant from the three vertices. 12. If JK = 10, then the locus of points in space that are 4 units from J and 5 units from K is a circle.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 11E: 11. (See Exercise 10.) According to Definition 5.29, is defined in by if and only if . Show that ...

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