2.4 Properties from Algebra and Proofs

20. If x + y = 9 and x - y = 12, then 2x = 21.

ADDITION

21. If AB - CD = EF - CD, then AB = EF.

ADDITION

14. If 1/2 m. angle F = 1/2 measure angle G, then m. angle F = m. angle G.

DIVISION

22c. x = -12

DIVISION

SET 22 and 24, TWO-Column Proof: Answer each question as in 19-21. Given the STATEMENT, what is the the REASON? If the statement comes from the Given statements for the problem, then the reason is "Given". Think of the next statement, (for example 2b.)as the conclusion from the hypothesis 2a, and the reason is written together with the statement in 2b. Thus, for #22, the REASON why 2/3 x = -8 is because BOTH sides was MULTIPLIED by 3. 22a. 2/3 x = -8GIVEN

GIVEN

22b. STATEMENT: 2x = -24

MULTIPLICATION

17. m angle A = m angle A

REFLEXIVE

13. If y = 2x + 3 and x = 2, then y = 7

SUBSTITUTION

16. If m. angle A = 90 and m. angle B = 90 then m angle A = m angle B.

SUBSTITUTION

#s 12 to 21, NAME the PROPERTY (write ONLY the name, so don't type "property of equality":)

SUBTRACTION

19. If AB + BC = 12, then BC = 12 - AB.

SUBTRACTION

18, If m angle 1 = m angle 2, m angle 1 = m angle 2.

SYMMETRIC

15. If AB + BC = AC and AC = EF + GH, then AB + BC = EF + GH.

TRANSITIVE