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