Midpoint and Distance
Q (0,10)
Find the distance between PQ
8
What are the next 3 numbers that would appear?
3,7,11,15,...
19, 23, 27
Write as a conditional statement.
When you are 18 you can vote.
If you are 18 then you can vote.
Inductive Reasoning
Reasoning that reaches conclusions based on a pattern of specific examples and past events.
Y (5,11)
Find the Distance of XY
8.94
What are the next 3 number that would appear?
101, 89, 77, 65,...
53, 41, 29
Write as a conditional statement.
A triangle with all angles congruent is equilateral.
If a triangle is equilateral then all angles are congruent.
Conjecture
A (3,-2)
B (12,15)
Find the distance of AB
9.24
What are the next 3 numbers that appear?
9, 6, 4, 8/3, ...
16/9 (1.78), 32/27 (1.19), 64/81(0.79)
Write as a conditional statement.
Alberto can go to the movies if he washes the car.
If Alberto washes the car then he can go to the movies.
Counter Example
An example that shows the conjecture is false.
C (-7,4)
D (13,-8)
Find the midpoint of CD
(3,-2)
Find the next 2 terms.
18, 24, 32, 128/3, ...
56.89, 75.85
Write as a conditional statement.
My hair will be shorter if I cut it.
If I cut my hair then it will be shorter.
Conditional
An if-then-statement that has a hypothesis following the if and a conclusion that follows the then.
T (5,-12)
P (11, 12)
Find the Mid-point of TP
(8,0)
What 3 number would appear next?
48, 36, 27, 20.25,...
15.1875, 11.39, 8.54
Write as a conditional statement.
Movie tickets are half off on Tuesday.
If the movie tickets are half off then it is Tuesday.
Inverse
If not p then not q