2.4 – Deductive Reasoning continued
Example 1 – Determine whether statement (3) follows from statements (1) and (2) by the Law of Detachment or the Law of Syllogism. If it does, state which law was used. If it does not, write invalid.
a. (1) If the sum of the squares of two sides of a triangle is equal to the square of the third side, then the triangle is a right triangle.
(2) For ; .
(3) is a right triangle.
b. (1) If Ling wants to participate in the wrestling competition, he will have to meet an extra three times a week to practice.
(2) If Ling adds anything extra to his weekly schedule, he cannot take karate lessons.
(3) If Ling wants to participate in the wrestling competition, he cannot take karate lessons.
2.5 – Postulates & Paragraph Proofs
· A postulate or axiom is a statement that is accepted as true.
POSTULATES2.1 / Through any two points, there is exactly one line.
2.2 / Through any three points not on the same line, there is exactly one plane.
Example 2 – Some snow crystals are shaped like regular hexagons. How many lines must be drawn to interconnect all vertices of a hexagonal snow crystal?
POSTULATES2.3 / A line contains at least two points.
2.4 / A plane contains at least three points not on the same line.
2.5 / If two points lie in a plane, then the entire line containing those points lies in that plane.
2.6 / If two lines intersect, then their intersection is exactly one point.
2.7 / If two planes intersect, then their intersection is a line.
Example 3 – Determine whether each statement is always, sometimes, or never true. Explain.
a. If plane T contains and contains point G, then plane T contains point G.
b. For , if X lies in plane Q and Y lies in plane R, then plane Q intersects plane R.
c. contains three noncollinear points.
L19 – pg 103 (21-25) & pg 108 (9 & 11-14)