2 . 2

PROPERTIES FROM ALGEBRA

PROSPERITIES OF ALGEBRA PG. 37

• Addition Property If a = b and c = d, then a + c = b +d .

• Subtraction Property If a = b and c = d, then a-c = b-d.

• Multiplication Property If a = b, then ca = cb.

• Division Property If a = b, and c ≠ 0, then =

• Substitution Property If a = b, then either a or b may be substituted for the other in any equation (or inequality).

• Reflexive Property a = a

• Symmetric Property If a = b, then b = a

• Transitive Property If a = b and b = c, then a = c

PROPERTIES OF CONGRUENCE

• Reflexive Property:• • <D <D

• Symmetric Property: • If , then

• Transitive Property: • If and , then • If <D <E and <E <F, then <D <F

• Distributive Property• a (b + c) = ab + ac

JUSTIFY EACH STATEMENT

• 1) If AB = CD and BC = BC, then AB + BC = CD + BC.

___________________

• 2) If m< A = ½ m<X and ½ m<X = m<B, then m<A = m<B ___________________

• 3) If point B is in the interior of <XOY, then m< XOB + m<BOY = m< XOY.

____________________• 4) If 2 + YZ = 8,

then YZ = 6._____________________

GEOMETRIC PROOF HINTS

• Worksheet

COMPLETE EACH PROOF

• Given m <1 = m< 3; m <2 = m <4• Prove m <ABC = m < DEF.

Statements Reasons

m <1 = m <3m <2 = m <4

m <1 + m <2 = m <3 + m <4

m<1 + m <2 = m <ABCm<3 + m <4= m<DEF

m <ABC = m <DEF

Given

Addition Property

Angle Addition Post.

Substitution Property

COMPLETE EACH PROOF

• Given ST = RN; IT = RU • Prove: SI = UN Statements Reasons

ST = RN

=SI + IT

= RU + UN

SI + IT = RU + UN

IT =RU

Given

Segment Addition Postulate

Substitution Property

Given

Subtraction PropertySI = UN

ST

RN

HINTS

• The first statement is almost always the statements that are provided.

• Your reasoning should be GIVEN for the first statement.

• The last statement is always the what we are trying to prove.

• Never use the word “prove” as a reason!

HOMEWORK

• pg. 41-42 WE #1-6