The ________ approach to management views workers as machine…
Questions
The ________ аpprоаch tо mаnagement views wоrkers as machine-like and emphasizes training them to follow the one best method for completing tasks. Chapter 10: Motivating Employees
Definitiоns, Axiоms аnd, Theоrems [3 pts eаch] The course begаn with a look at what constitutes an axiomatic system. We learned of four basic properties that all such systems have. State these here [4 pts each] State the definition of each of the following terms. (xcong ypmod{2pi}) angle of parallelism for a point and a line the defect of a triangle hyperbolic area of a polygonal region [4 pts each] In our course, you have seen how the concept of parallelism has branched the study of geometry into different directions. State the following parallel postulates: Euclid's Fifth Postulate Playfair's Parallel Postulate Hyperbolic Parallel Postulate [4 pts each] We have studied at least three different named axiom systems, which demonstrate various ways of approaching geometry, namely Hilbert's Birkhoff's, and SMSG's. Below you will state a specific axiom of each. State Hilbert's Order Axiom II-4 (equivalent to Pasch's Lemma). State Birkhoff Postulate I (the ruler postulate) State SMSG Postulate 9 (plane separation postulate) [4 pts each] Finally, we have a couple of important theorems. State the Crossbar Theorem. State the Saccheri-Legendre Theorem. Proofs Each proof is worth 10 points for a total of 80 points. The previous part contained a total of 60 points. Incidence Geometry Recall the axioms of an incidence geometry: There is exactly one line on any pair of distinct points. Every line has at least two distinct points on it. There are at least three distinct points. Not all points lie on the same line.Prove: In an incidence geometry, each point has at least two lines on it. Neutral Geometry The following three proofs are in the context of Neutral Geometry. No parallel axioms are assumed. (The External Angle Theorem - Neutral Geometry): Given a triangle (triangle ABC) with exterior angle (angle BCD), prove: the measure of (angle BCD) is greater than the measure of angle (angle ABC). (ASA Congruence Theorem - Neutral Geometry): Given (triangle ABC) and (triangle DEF), with (angle BACcong angle EDF), (overline{AC}cong overline{DF}), and (angle BCAcongangle EFD), prove: (overline{AB}congoverline{DE}). [The figure includes a hint.] Given Saccheri quadrilateral (ABCD), with base (overline{AB}), prove: the diagonals are congruent, and the summit angles are congruent. That is, (overline{AC}congoverline{BD}) and (angle ADCcong angle BCD). Euclidean Geometry The following two proofs are in the context of Euclidean geometry. Given parallelogram (ABCD), where (ABparallel CD) and (ADparallel BC), prove: (overline{AB}congoverline{CD}) and (overline{AD}congoverline{BC}). Given triangle (triangle ABC), with right angle at (C), and side lengths (AB=c), (BC=a), and (AC=b), prove (using similarity) that (a^{2}+b^{2}=c^{2}). Be sure to explain why the triangles you use are similar. Hyperbolic Geometry The following two proofs are in the context of hyperbolic geometry. (Hyperbolic AAA Congruence) Given triangles (triangle ABC) and (triangle DEF), with (angle Acongangle D), (angle Bcongangle E), and (angle Ccongangle F), prove: (triangle ABCcong triangle DEF). The figure gives a hint. Given Lambert quadrilateral (ABCD), with right angles at (A), (B), and (D), prove: (BC>AD). (You may assume the angle at (C) is acute.) Once again, the figure contains a hint.