WARM UP Please pick up the worksheet on the cart and complete the 2 proofs.

1. WARM UP Please pick up the worksheet on the cart and complete the 2 proofs.

2. REVIEW SECTIONS 2.1 – 2.3

3. Section 2-1 A statement in the form “If _____, then _______.” is called a conditional statement. A conditional statement has two parts: The clause that comes directly after the “if” is called the hypothesis. The clause that comes directly after the “then” is called the conclusion. Example: If you were born in July, then you were born in the summer. Hypothesis: You were born in July. Conclusion: You were born in the summer.

4. To find the converse of a conditional statement, you must switch the hypothesis and conclusion. If you were born in July, then you were born in the summer. Converse: If you were born in the summer, then you were born in July. If you want to state that a converse is false, you must provide a counterexample. A counterexample is an example for which the hypothesis is true, but the conclusion is false. Counterexample: You were born in June.

5. If a conditional and its converse are both true they can be combined into a single statement by using the words “if and only if.” A statement that contains the words “if and only if” is called a biconditional. If today is Monday, then yesterday was Sunday. Rewrite: Today is Monday, if and only if, yesterday was Sunday.

6. Section 2-2 C EXAMPLE 1: Given: mÐ1 = mÐ3 Prove: mÐAEC = mÐBED B 1 A 2 3 D E Statements Reasons 1. Given • mÐ1 = mÐ3 • mÐ1 + mÐ2 = mÐ2 + mÐ3 • 3.mÐAEC = mÐ1 + mÐ2 mÐBED = mÐ2 + mÐ3 • 4. mÐAEC = mÐBED 2. Addition Property 3. Angle Addition Postulate 4. Substitution

7. EXAMPLE 2: Given: AB = BC; BD = BE Prove: AD = CE C A B D E Statements Reasons 1. Given • AB = BC; BD = BE 2. AB + BD = BC + BE 2. Addition Property • AB + BD = AD • BC + BE = CE 3. Segment Addition Postulate 4. AD = CE 4. Substitution

8. Section 2-3 Definition of Midpoint Midpoint Theorem If M is the midpoint of AB, then AM = ½AB and MB = ½AB. If C is the midpoint of AB, then AC @ CB. Def. of Angle Bisector Angle Bisector Theorem If WY is the bisector of ÐXWZ, then mÐXWY = ½mÐXWZ and mÐYWZ =½mÐXWZ. A ray that divides an angle into two congruent adjacent angles. ÐXWY @ÐYWZ

9. Given: B is the midpoint of AC; C is the midpoint of BD. Prove: AC = BD A B C D 1. B is the midpoint of AC 1. Given C is the midpoint of BD 2. AB = BC; BC = CD 2. Def. of a Midpoint 3. AB = CD 3. Substitution/Transitive 4. AB + BC = CD + BC 4. Addition Property 5. AB + BC = AC BC + CD = BD 5. Segment Add. Post. 6. AC = BD 6. Substitution