Presentation on theme: "This lesson defines what a proof is and shows how to write a proof for a given hypothesis and conclusions."— Presentation transcript:
This lesson defines what a proof is and shows how to write a proof for a given hypothesis and conclusions.
You will be able to identify the postulates, axioms, and theorems that justify the statements in a proof. You will be able to use a theorem to solve problems.
Theorem: A cat has nine tails. Proof: No cat has eight tails. A cat has one tail more than no cat. Therefore, a cat has nine tails.
Proof – A series of true statements leading to a desired conclusion Theorem – A statement that can be proven true Given – Specified Prove – To show that a conclusion is true
If Angles are vertical angles, then their measures are equal. To start a proof, clearly state what is given and is to prove. Given or hypothesis: “angles are vertical” Conclusion: “their measures are equal”
Next, draw a picture of the given. a b c l d m a and d are vertical angles c and b are vertical angles
To Prove: m a = m d m c = m b Work in 2 columns. You are now ready.
Statement Lines l & m intersect to form vertical angles a & d m a + m b = 180 o m d + m b = 180 o Proof 1.Given 2. a & b are adjacent on m and are supplementary 3. b and d are adjacent on l and are supplementary
m a + m b = m b + m d m a = m d 4)Axiom I, substitution and steps 2 & 3 5)Axiom 3, if equals are subtracted from equals, the differences are equal