Definitions
The process of reasoning that a rule or statement is true because several specific cases are true
Inductive reasoning
Perimeter of a rectangle
P = 2L + 2W
P = a + b + c
Find the perimeter of a rectangle if
L = 14 ft., W = 10 ft.
P = 48 ft.
If it is 50oF, what is the temperature in degrees Celsius?
10oC
A statement that is believed to be true (if proven, it becomes a theorem)
Conjecture
A = LW
d = |a2 - a1|
Find the perimeter of a triangle if:
a = 29 in., b = 14 in., c = 18 in.
P = 61 in.
If a six-sided figure has lengths that are all equal to 10 in., find the perimeter.
P = 60 in.
An example that does not support a conjecture
Counterexample
Area of a triangle
A = 1/2 BH
Distance formula (between two points on a coordinate plane)
d = sq.rt. [ (x2 - x1)2 + (y2 - y1)2 ]
Find the area of a rectangle if:
L = 90 yd., W = 43 yd.
A = 3,870 yd.2
Find the distance between 19 and -4 on a number line
d = 23 units
A mathematical relationship expressed with symbols
Formula
Pythagorean Theorem
a2 + b2 = c2
(EXTRA - not in the text)
Area of a square
A = s2
Find the area of a triangle if:
b = 16 m, h = 15 mA = 150 m2
Find the distance between (3, 2) and (9, -6) on the coordinate plane
d = 10 units
The sum of the side lengths of a closed geometric figure
Converting Fahrenheit to Celsius
C = 5/9 (F - 32)
(EXTRA - not in the text)
Converting from Celsius to Fahrenheit
F = 9/5 C + 32
Find the length of the hypotenuse of a right triangle if:
a = 15 cm, b = 8 cm
c = 17 cm
Complete the following conjecture:
The product of an even and odd number is ____
even