October 02, 2015
October 02, 2015
(2.6) Algebraic Proof
Objective: Use algebra to write two-column proofs and use
properties of equality to write geometric proofs.
Why: You can prove various forms of equation conversions are
true and you can validate geometric conjectures.
October 02, 2015
Obj:
Use algebra to write two-column proofs and use
properties of equality to write geometric
proofs.
Solve the formula below for F.
C=
5
9
(F - 32)
October 02, 2015
Obj:
Use algebra to write two-column proofs and use
properties of equality to write geometric
proofs.
Properties of Equality
addition: you can add the same thing to both sides of the equ.
subtraction: you can subtract the same thing from both sides of the equ.
multiplication: you can multiply both sides of an equ. by the same number
division: you can divide both sides of an equ. by the same number.
reflexive: anything equals itself (a = a)
symmetric: you can switch all items with respect to the equal sign
(If a = b, then b = a)
transitive: if 2 items equal the same item, then the two items equal each
other (If a = b and b = c, then a = c)
substitution: an equivalent item may be substituted in for something
distributive: a(b + c) = ab + ac
Properties of Congruence:
Reflexive:
EF
EF,
Symmetric: If 1
Transitive: If AB
A
A
2, then 2
CD and CD
1
EF, then AB
EF
October 02, 2015
Obj:
Use algebra to write two-column proofs and use
properties of equality to write geometric
proofs.
Solve 2(5 - 3a) - 4(a + 7) = 92
for each step.
and then write a justification
October 02, 2015
Obj:
Try this:
Use algebra to write two-column proofs and use
properties of equality to write geometric
proofs.
Solve -5(x + 4) = 70 and provide a justification for each step.
October 02, 2015
Obj:
Use algebra to write two-column proofs and use
properties of equality to write geometric proofs.
Write a two-column proof to verify the conjecture:
If
FGJ =
JGK
and
JGK =
KGH, then x = 6.
J
K
(6x + 7)o
F
G
(8x - 5)o
H
October 02, 2015
Obj:
Use algebra to write two-column proofs and use
properties of equality to write geometric
proofs.
HW
HR (2.6) Pg.139: 9-17, 19, 21, 37