Postulates – Day 2

1. Postulates – Day 2

2. REFLEXIVE ab = ab

3. TRANSITIVE a = b, b = c, so a = c

4. SUBSTITUTION a = 2b, b=c, so a=2c

5. SYMMETRIC ab = ba

6. The Partition Postulate 3.5 • A whole is equal to the sum of its parts. • A B C D • AB + BC = AC • Also true for angles

7. The Addition Postulate 3.6 • If equal quantities are added to equal quantities, the sums are equal. • If a = b and c = d, then a + c = b + d • True for any quantities including line segments and angles.

8. The Subtraction Postulate 3.7 • If equal quantities are subtracted from equal quantities, the differences are equal. • If a = b, and c = d, then a – c = b –d • True for any quantities including line segments and angles.

9. Proof Practice: pg 122 #3 • Given: • AED and BFC • AE = BF • ED =FC E F FF • Prove: AD = BC A B D C

10. Fill in the blanks REASON • . • . • . • . • . STATEMENT • AED and BFC are line segments • AE = BF • ED = FC • AE + ED = BF + FC • AD = BC

11. Proof Practice #2 pg 123 #4 • Given: SPR = QRP and RPQ = PRS • Prove: SPQ = QRS Q P R S

12. Fill in the blanks REASONS 1. Given 2.If congruent angles are added to congruent angles, the sums are congruent. (addition) 3. STATEMENTS 1. 2. 3. SPQ = QRS