Proofs Much of the enjoyment and challenge of geometry is found in "proving things!" Two column proofs are the most common type of proof that we will  use.

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Presentation transcript:

Proofs Much of the enjoyment and challenge of geometry is found in "proving things!" Two column proofs are the most common type of proof that we will  use this year. All two column proofs have the following elements: "Given" statements "Prove" statement A diagram Two column: Statements and Reasons Every statement and reason is numbered

Definitions Index Card!! need to be stated in If - then Form are reversible Example: Rt = 90 If an is a 90 , then it is a rt . If an is a rt , then it is a 90 . Index Card!!

Statements Always write a given for the 1st statement Statements need to be in a logical order Statements are specific The LAST statement is the "Prove" Index Card!!

Reasons Index Card!! "Given" is always the 1st Reason Definitions written in "if-then" form (they are reversible!) Theorems / Postulates (written out) "Addition"/ "Subtraction" "Assumed from diagram" "Same as _____" Index Card!!

Sample Problems 1. Given: See page 25 in your textbook for Sample Problems #1 - 3 A B C D 1. Given: Statements   Reasons 1. Given 2. Given 3. If two angles are right angles, then they are  congruent. 1. 2. 3. Prove:

2. Given: Diagram as shown Conclusion: E J F H G 1.  Diagram as shown   1. Given 2. is a straight angle.  2. Assumed from diagram 3.  3. Assumed from diagram 4. 4. If two angles are straight angles, then they are congruent. Statements Reasons

Statements Reasons Addition (50 + 40 = 90) 3. Given: R T Prove: S X V 1. 2. 3. 4. 5. 6. Given Addition (50 + 40 = 90) If an angle is 90 deg, then it is a rt angle If two angles are rt angles, then they are  congruent. Statements Reasons

Exit Slip 1. List 3 "reasons" for proofs 2. What does bisect mean? 3. If two points are trisection points, what can you conclude?

Switch to the Midpoints and Bisectors Power Point!