2.3 notes and assignment 9-15-2014

September 15, 2014
1) If xy = 144, x + y = 30, and x > y, what is the value of x – y ?
y=30 -x
Bellringers
x(30 -x) =144
x = 24, y =6 x-y = 18
30x -x 2 = 144
0 = x2 - 30x +144
(x -24) (x+6) = 0
x = 24 , x = -6
2) Given m<5 = m<6; m<7 = m<8
Prove: m<ABC = m<ACB
A
7
5
6
8
B
1)
1) given
2) m<ABC = m<7 + m<5
m<ACB = m<6 + m<8
2) angle addition post
3) m<7+m<5 = m<6 +m<8
3) addition post
4) m< ABC = m<ACB
4) substitution
Standards: G.CO.9
1) I can prove theorems about lines and
angles.
2) I can restate the angle bisector theorem
and the midpoint theorem in my own words.
3) I can create a diagram of given
information and construct a proof using
definitions, postulates, and theorems that I
have already learned.
C
September 15, 2014
HOMEWORK ANSWERS:
1) given, add prop of =, div prop of =
3) given, Mult prop of =, subtraction prop of =
5) given, mult prop of =, distributive, add prop of =, div prop of =
7) Angle addition postulate, angle addition postulate,
m<AOD = m<1 + m<2 +m<3, substitution prop
8) FL = AT, Reflexive prop, addition prop of =, segment addition post, FA=LT
10) given, angle addition post, substitution prop, reflexive prop, M<5=m<6;
subtraction prop of =
12 and 14 - students put on board
11 & 13 see back of book
12)
September 15, 2014
Reasons used in Proofs
***Given Information
***Definitions
***Postulates or Properties
***Theorems that have already been proven
September 15, 2014
2.3 Proving Theorems
A
Theorem 2.1 Midpoint Theorem
If M is the midpoint of AB, then AM = 1 AB and MB = 1 AB
2
2
In book
M
B
Prove this: Given M is the midpoint of AB
Prove AM = 1/2 AB; MB = 1/2 AB
Statements
Reasons
***********************************************************************************
1) M is the midpoint of AB
1) Given
2) AM = MB
3) AM + MB = AB
4)
2) Definition of midpoint
3) segment addition
AM + AM = AB or 2AM = AB
5) AM = 1/2AB
4) substitution
5) Division property
6) MB = 1/2AB
6) subtitution
Theorem 2.2 ANGLE BISECTOR THEOREM
A
If BX is the bisector of ABC, then
m ABX = 1/2 m ABC and m XBC = 1/2 ABC
X
B
********************************************************************************
C
Given BX is the bisector of ABC.
#10 classroom exercises
Prove: m ABX =1/2m ABC; m XBC = 1/2m ABC
Statements
Reasons
Given
1)
1)
2) m<ABX = m<XBC
2)
3) m<ABX + m<XBC = m<ABC
3)
Angle addition post
4) m<ABX + m<ABX = m<ABC (2m<ABX = m<ABC)
4)
substitution prop
5) m<ABX = 1/2m<ABC
5)
mult. prop of =
6) m<XBC = 1/2m<ABC
Def. of angle bisector
6)
substitution prop (steps 2 and 5)
September 15, 2014
Guided Practice
Given: EG is the bisector of DEF; SW is the bisector of RST;
m DEG = m RSW
D
Prove: m DEF = m RST
E
G
S
R
W
F
T
****************************************************************************
Statements
Reasons
1)
2)
EG is the bisector of DEF; SW is the bisector of
m DEG = m RSW
m<DEG = 1/2m<DEF
m<RSW = 1/2m<RST
3) 1/2m<DEF = 1/2m<RST
4)
m<DEF = m<RST
"I can do this proof
in three steps"
A
2)
Angle Bisector Theorem
3)
substitution
Given: m 1 = m
2;
AD bisects CAB;
BD bisects CBA
Prove: m 3 = m 4
C
3
1) Given
4) Multiplication prop of =
YOUR TURN
1
RST;
D
4
2
B
September 15, 2014
2.3 Round Table Consensus (use as bellringer next day if necessary)
Assignment page 45 CE 1-9
WE 9-11, 13, 14, 17-19
Algebra Review
Due Friday!
September 15, 2014
CE 1-9 page 45
Homework answers
1) angle add post. 2) segment Add post. 3) angle add post
4) def of midpt
5) midpoint theorem
6) and 7) Definition of segment bisector
WE 9-11, 13, 14, 17-19 page 46
9) 60 10) 75 11) 70
13) 12, 28, 6, 22
14) 18, 54
17) AC =BD
18) AC = BD and AE=DE=CE=BE
19) Given, Ruler Postulate, given, def of midpoint, substitution prop,
a + b, addition prop of =, division prop of =

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