Definitions
What is conjecture?
A statement that is believed to be true.
What type of reasoning is being used? What comes next?
Fall, Winter, Spring...
Inductive Reasoning.
Summer.
Name the property.
a=a
Reflexive Property of Equality
Point E is between points D and F. If DE = x+3, EF = 4x-10, and DF = 10x−2, find x.
x=3
What is counterexample?
An example that shows a conjecture to be false.
Finish this inductive reasoning pattern.
1/2, 2/6, 3/18, 4/54, ____
5/162
Name the property.
If a=b, then a-c = b-c.
Subtraction Property of Equality
Y is the midpoint of XZ. If XZ = 12x + 5 and YZ = 8x - 2, find x.
x=-9/4
What is a linear pair?
A pair of adjacent angles whose non common sides are opposite rays. It's supplementary and equals 180°.
Use deductive reasoning to solve the following.
14=3x-4
x=6
Name the property.
If a=b, then b=a.
Symmetric Property of Equality
̅
→SV is an angle bisector of ∠RST. If m∠RSV = (3x + 5)° and m∠RST = (8x − 14)°, find x.
x=12
The process of using logic to draw conclusions. By using math to solve.
Use deductive reasoning to solve the following and name the Property of Equality.
3-4x=-5
x=2
Name the property.
If a=b and c≠0, then a/c = b/c.
Division Property of Equality
∠ABC and ∠CBD are a linear pair. If m∠ABC = m∠CBD = 3x - 6, find x.
x=32
What is a theorem?
A statement that you can prove is true using a series of logical steps.
Identify the IF and THEN in the conditional statement.
"You must wear your jacket if it's cold outside."
IF it's cold outside, THEN you must wear your jacket.
Name the property.
If a=b and b=c, then a=c.
Transitive Property of Equality
Given: RT = 5x - 12
Use the Segment Addition Postulate.
RS + ST = RT
(x + 2) + (3x - 8) = 5x - 12
x=6