Postulates and Paragraph Proofs Eric Hoffman Advanced Geometry

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Postulates and Paragraph Proofs Eric Hoffman Advanced Geometry PLHS Oct. 2007

Postulates and Paragraph Proofs Eric Hoffman Advanced Geometry PLHS Oct. 2007

Key Topics • Postulate or Axiom: a statement that describes a fundamental relationship between

Key Topics • Postulate or Axiom: a statement that describes a fundamental relationship between basic terms in Geometry – Ex. Through any two points there is exactly one line – Ex. The shortest distance between any two points is a line • These statements are always accepted as true

Key Topics • These are essential in writing proofs for this chapter

Key Topics • These are essential in writing proofs for this chapter

Using Postulates • Determine whether each statement is always, sometimes, or never true using

Using Postulates • Determine whether each statement is always, sometimes, or never true using our knowledge about postulates. • If plane T contains and then plane T contains point G • For , if X lies in plane Q and Y lies in plane R then, plane Q intersects plane R • contains three non-collinear points

Key Topics • Theorem: a statement or postulate that has been shown to be

Key Topics • Theorem: a statement or postulate that has been shown to be true • Once proven true, a theorem can be used like a statement or postulate to justify that other statements are true

Key Topics • Proof: a logical argument in which each statement you make is

Key Topics • Proof: a logical argument in which each statement you make is supported by a statement that is accepted as true (can be a axiom, postulate, theorem) • Paragraph Proof: a type of proof in which you write a paragraph to explain why a conjecture is true for a given situation

All paragraph proofs should start with what is given and what we want to

All paragraph proofs should start with what is given and what we want to prove Proofs should end with a box which denotes the end of your proof

Key Topics • In the figure E is the midpoint of AB and CD,

Key Topics • In the figure E is the midpoint of AB and CD, and AB = CD. Write a paragraph proof to prove that AE ED

Key Topics • Given: E is the midpoint of AB and CD, and AB

Key Topics • Given: E is the midpoint of AB and CD, and AB = CD • Prove: AE ED Proof: Since E is the midpoint of AB by the Midpoint Theorem we know that AE EB, similarly we know that CE ED. By the definition of congruent segments we know that AE = EB = ½ AB, similarly we also know that CE = ED = ½ CD. Since we know that AB = CD, by the multiplication property we can say that ½ AB = ½ CD, and thus AE = ED. Therefore by the definition of congruent segments AE ED □

Key Topics • Homework pg. 91, 92 10 – 30 even 11 problems!!

Key Topics • Homework pg. 91, 92 10 – 30 even 11 problems!!