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Lesson 2-5. Postulates and Paragraph Proofs. Ohio Content Standards:. Ohio Content Standards:. Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.
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Lesson 2-5 Postulates and Paragraph Proofs
Ohio Content Standards: Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.
Ohio Content Standards: Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects.
Ohio Content Standards: Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof.
Postulate Statement that describes a fundamental relationship between the basic terms of geometry.
Postulate 2.1 Through any two points, there is exactly one line.
Postulate 2.2 Through any three points not on the same line, there is exactly one plane.
Postulate 2.3 A line contains at least two points.
Postulate 2.4 A plane contains at least three points not on the same line.
Postulate 2.5 If two points lie in a plane, then the entire line containing those points lies in that plane.
Postulate 2.6 If two lines intersect, then their intersection is exactly one point.
Postulate 2.7 If two planes intersect, then their intersection is a line.
Determine whether each statement is always, sometimes, or never true. Explain.
Determine whether each statement is always, sometimes, or never true. Explain. If plane T contains EF and EF contains point G, then plane T contains point G.
Determine whether each statement is always, sometimes, or never true. Explain. For XY, if X lies in plane Q and Y lies in plane R, then plane Q intersects R.
Determine whether each statement is always, sometimes, or never true. Explain. GH contains three noncollinear points.
Theorem A statement or conjecture that has been shown to be true.
Proofs A logical argument in which each statement you make is supported by a statement that is accepted as true.
Paragraph Proof You write a paragraph to explain why a conjecture for a given situation is true.
Five essential parts of a good proof: 1) State the theorem of conjecture to be proven.
Five essential parts of a good proof: 2) List the given information.
Five essential parts of a good proof: 3) If possible, draw a diagram to illustrate the given information.
Five essential parts of a good proof: 4) State what is to be proved.
Five essential parts of a good proof: 5) Develop a system of deductive reasoning.
Theorem 2.8 If M is the midpoint of AB then AM MB.
Given AC intersecting CD, write a paragraph proof to show that A, C, and D determine a plane.
