2.2 day 2 notes with proofs 9-12-2014

1)
Bellringers
2
x = -5 implies x = 25
True or False
Hypothesis:
Conclusion:
Converse:
Inverse
Contrapositive
True or False
STATEMENTS
REASONS
1) 3/4x = 6 + 2x
1)
2) 3x = 4(6+2x)
2)
3) 3x = 24 + 8x
3)
4) -5x = 24
4)
5)
5)
x = -24/5
Warm up
Homework answers page 40 CE 1-12
1) Identify the hypothesis and the conclusion of:
a2 >16 if a > 4
2) Provide a counter example to show the statement is false:
If a number is divisible by 4, then it is divisible by 6.
3) A math student showed the following work on his/her paper.
3a = 24
so a = 8
What property did this student use to arrive at his/her answer?
1) Reflexive prop of congruence
congruence
3) Symmetric property of equality
equality
2) Transitive Property of
4) Subtraction property of
5) Division prop of =
6) Mult. prop. of =
7) Distributive prop of =
8) Addition prop of =
9) substitution prop
10) transitive prop of =
11)
Given
12) 1) Given 2) ST, RN Seg Add Post
Addition prop of =
3) substitution prop
Angle addition postulate
4) given
substitution property
5) SI = UN; Subtraction prop of =
Algebra Review Questions
Proof
Given: m AOC = m
Prove: m 1 = m 3
B
BOD
A
12 3
O
STATEMENTS
1)
REASONS
1) GIVEN
C
D
Note: there is NO substitution property of congruence. Substitution
deals with number, not congruence!!!
D
Given: AB and CD intersect
A
B
XY ≅ AB
C
X
We cannot substitute XY for AB and
assert that XY and CD intersect.
Y
1)
1) Given
1)
1) Given
2) EF = FG
2) transitive property of congruence
2) m<1 + m<2 = m<3 + m<4
3) m<1 + m< 2 = m<ABC
m<3 + m<4 = m<FED
4) m<ABC = m<FED
2) Addition property
3) angle addition
3) F is the midpoint of EG
3) definition of midpoint
4) Substitution
Statement
Reasons
1)
1) Given
2) AB + BC = AC
2) segment addition
BC + CD = BD
3) BC = BC
3) Reflexive property
4) AB = CD
4) Definition of congruence
5) CD + BC = AC
5) substitution
6) AC = BD
6) substitution
7) AC = BD
7) Definition of congruence
Statements
Reasons
1) OM = OW; O is midpoint of MN
1) Given
2) ON = OM
2) Definition of midpoint
3) ON = OW
3) substitution
1)
1) Given
2) <1
<2
2) definition of angle bisector
3) <2
<3
3) transitive
m<JOL
m<KOM
1)
1) Given
2) m<1 + m<2 = 180
2) angle addition
3) 90 + m<2 = 180
3) substitution
4) m<2 = 90
m<JOL
m<JOM = m<KOM
4) subtraction property
answers to proofs -- students put on the white board
Exit Ticket
Name: ______________
1) Name the property that justifies the following statement:
If <A = <B and <B =<C, then <A = <C
transitive property of congruence
2) Name the property that justifies: 4(x +z) = 4x + 4z
distributive property
3) Name the property that justifies:
If x = 3 and x + y = 7, then 3 + y = 7
4) Give an example of the reflexive property.
substitution
m<4 =m<4
symmetric
equality
5) If y + 3 = x, then x = y + 3 is an example of the _______ property of _______.
Multiplication
equality
6) If AB = 1/2(AC), then 2AB = AC is an example of the _____ property of _______
Exit Ticket
Name: ______________
1) Name the property that justifies the following statement:
If <A = <B and <B =<C, then <A = <C
2) Name the property that justifies: 4(x +z) = 4x + 4z
3) Name the property that justifies:
Assignment
page 40 CE 11 and 12
page 41 WE 1-7 odd
8, 10-14 all
If x = 3 and x + y = 7, then 3 + y = 7
EXPLAIN
4) Give an example of the reflexive property.
IF...Then
Advertisement Project
5) If y + 3 = x, then x = y + 3 is an example of the _______ property of _______.
6) If AB = 1/2(AC), then 2AB = AC is an example of the _____ property of _______
Due Monday, September 22nd

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