Justify each step for the algebraic proof. Given: Prove: 2. Given: −20=−4−6 Prove

[Pages:2]Geometry 2.4 worksheet #2

Justify each step for the algebraic proof.

1. Given: 3 - 7 = 20

Prove: x = 9

Given

3 - 7 + 7 = 20 + 7 3 = 27 Simplify

)* = +,

))

Name: ____________________________

2. Given: -20 = -4 - 6 -20 = -4 - 6 -20 = -10

2+3 = 243*

243 243

-2 =

Prove: x = -2

= 9

Simplify

= -2

Solve each equation. Justify each step of the algebraic proof. 3. Given: 8x - 2 = -9 + 7x Prove: x = - 7 4. Given: 24 = -4 (5 - 1) Prove: x = - 1

a.

a.

a.

a.

b.

b.

c.

c.

d.

d.

b.

b.

c.

c.

d.

d.

e.

e.

e. 4. Given: :;< = 8

)

a.

e.

Prove: v = 15

a.

b.

b.

c.

c.

d.

d.

f.

f.

4. Given: - -12 + 4 - 3 = -7 Prove: x = - 4 )

a.

a.

b.

b.

c.

c.

d.

d.

e.

e.

e.

e.

f.

f.

Write the letter of the property that justifies each statement.

______ 5. If 10 + = 32 and = 3, then 4 + 3 = 7

______ 6. =

______ 7. If = -2, then 2 = -4

______ 8. If 6 = 54, then = 9

______ 9. If 3 = , then = 3

______10. If + = 14, then + - 5 = 14 - 5

)

)

______11. - = , then, = +

______12. ( + ) = +

______13. If + = and = 2, then + = 2

A. Addition Property of Equality B. Subtraction Property of Equality C. Multiplication Property of Equality D. Division Property of Equality E. Distributive Property F. Substitution Property G. Reflexive Property H. Symmetric Property I. Transitive Property

Write a two-column proof for each problem.

14. Given: = -13 + 2

= 6

= + 2

Prove: = 9

Statement

Reason

a.

a. given

b.

b. given

c.

c. given

d. + =

d.

e.

-13 + 2 + 6 = + 2

f.

e. f. Simplify

g. 2 - 7 = + 2

g.

- -

h.

h.

15. Given: = 3 - 4

= 40

F is the midpoint of GH

Prove: x = 8

Statement

Reason

a.

a. given

b.

b. given

c.

c. given

d.

d.

e. f. + = 40

e. Definition of congruency f.

g. + = 40

g.

h. 3 - 4 + 3 - 4 = 40 h.

i. 6 - 8 = 40

i. Simplify

j.

j.

g. i. x = 9

g. Addition property

of equality

k. 6 = 48 l. m.

k. Simplify

i. Division property of equality m.

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download