3-1: Conjectures & Counterexamples
3-2: Statements, Cont., Bicond.
3-2: Statements, Cont., Bicond.
Patterns and Conjectures:
What is the next pattern?
8:00am, 8:30am, 9:00am, 9:30am.......
10:00 am
What is deductive reasoning?
AND!!!!!
Deductive reasoning or Inductive reasoning.....
A dental assistant notices that a patient has never been on time for an appointment she concludes that the patient will be late for her next appointment.
General facts, rules and definitions
Inductive reasoning
Writing correct statements and reasons:
Chip draw two line segments: (X)
Given: J is the Midpoint of RC
J is the midpoint of LM
RC is congruent to LM
Prove: line segment RJ is congruent to LM
Statements Reasons
1 J is the midpoint of RC Given
J is the midpoint of LM
RC is congruent to LM
2 RJ=JC Definition of midpoint
LJ=JM
3 RC=LM Definition of Segments
4 RC=RJ + JC Addition Postulate
LM=LJ + JM
5 RJ + JC = LJ + JM Substitution
6 RJ + RJ = LJ + LJ Substitution
7 2RJ = 2LJ Simplify
8 RJ = CD Division Prop.
9 RC is congruent to LM Definition of Segments
Three segments parallel to line segment AE
SHOW PICTURE!!!!!!!!!!!!!!
BF, CG, DH
Show picture!!!!!!!!!!!!
State the postulate or theorem that justify your answer.The measure of angle 3 is congruent to the measure of angle 7
Alternate interior angles converse
Make a conjecture (odd or even)
The product of two and a number, plus one is
Odd
Deductive reasoning or Inductive reasoning??
A person must have a membership to work out at a gym. Jessie is working out at that gym. Jessie has a membership to that gym
Deductive
Which Postulate??
AB + BC = AC
Addition postulate
Identify the transversal connecting each pair
SHOW PICTURE!!!!!!!
Angle 5 and Angle 15
Alternate exterior
Find the value of x
Show picture!!!!!!!
6
Make a conjecture about the table:
x y
1st 20
2nd 60
3rd 100
4th 140
5th ????
180
Is the conclusion valid??
Given: All vegetarians do not eat meat. Theo is a vegetarian.
Conclusion: Theo does not eat meat
Valid
Properties of segment congruence
LM = OP, and OP = QR, then QR = LM
Transitive property
SHOW PICTURE!!!!!!!!!!
In the figure the measure of angle 3 is 75 degrees and the measure of angle 10 is 105 degrees.
Find the measure if the angle
Find the measure of angle 5
105
Find the value of x so that L is parallel to m
SHOW PICTURE!!!!!!!!
20
Compound statements using the word and is???
Compound statement using or is????
Conjectures
Disjunction
Sometimes, never or always?? AND!!!! What postulate
Line m contains only point B
NEVER!!!! Postulate 3.3
Chip is installing shelves in his room. One of the brackets he chose for himself. if mL3= 65 degrees what is mL4??
(which theorem and property?)
mL3 + mL4 = 180 ___________________
65 + mL4 = 180 ___________________
mL4 = 115 __________________
Supplementary Theorem
Substitution
Subtraction
The product of two lines that equal -1 is what????
Perpendicular
Find the distance between point P and line L
Line L contains points (0,-3) and (7,4)
Point P (4, 3)
Square root of 2 or 1.41
What is the hypothesis and conclusion of this conditional statement?
If there is no struggle, there is no progress
H: there is no struggle
C: there is no progress
answers may vary
Two-Column proof
Chip draw a line segment!!!
Given: J is the midpoint of line segment RC
Prove: line segment RJ is congruent to line segment JC
Statements Reasons
J is the midpoint Given
RJ is equal to JC Definition of midpoint
RJ is congruent to JC Definition of congruence
Find the measure of angle ABC and CBD
SHOW PICTURE!!!!!!
ABC = 36
CBD = 84
Determined whether line AB and CD are perpendicular, parallel or neither
A(1,5) B(4,4), C(9,10) D(-6,-5)
Parallel
Find the distance between each pair of parallel lines
y=7
y=-1
8