Math Chapter 2

an unproven statement that is based on observations

when you find a pattern in specific cases and then wright a conjecture for the general cause

a specific case for which the conjecture is false

• 2(-1)>-1
• -2>-1 False

• a logical statement that has 2 parts, a hypothesis and a conclusion. It is written in a
• if-then form

a statement that contains the phrase "if and only if"

• Example: an angle is a right angle if and only if its angle measurement is equal to
• 90 degrees

• if hypothesis A, then conclusion B
• if hypothesis B, then conclusion C
• if hypothesis A, then conclusion C

Law of Detachment ( also known as Modus Ponens (MP) ) says that if p=>q is true and p is true, then q must be true.

• example:If an angle is obtuse, then it cannot be acute.
• Angle A is obtuse.
• ThereforeAngle A cannot be acute.

The points of a line can be matched one to one with the real numbers. The real numbers that correspond to a point is the coordinate

• If B is between A and C, then AB+BC=AC
• If AB+BC=AC, then B is between A and C

If P is in the interion of <RST, then the measure of <T=RST is equal to the sum of the measure of <RSP and <PST

Through any two points there exists exactly one line

A line contains at least two points

If two lines intersect, then their intersection is exactly one point

through any three noncolinear points there exists exactly one plane

A plane contains at least three noncolinear points

If two points lie in a plane, then the line containing them lies in the plane

If two planes intersect, then their intersection is a line

a line perpendicular to a plane if and only if the three line intersects in a point ane is perpendicular to every line in that planethat intersects it at that point

If a=b, then a+c=b+c

If a=b, then a-c=b-c

If a=b, then ac=ab

If a=b and c is not equal to 0, then a/c=b/c

If A=b, then "A" can be subsituted for b in any equation or expression

a(b+c)=ab+ac, where a, b, and c, are real numbers

A=A

If a=b, then b=a

If a=b and b=c, then a=c

All right angle are congruent

If two angles are supplementry to the same angle, then they are congruent

If two angles are complementry to the same angle , then they are congruent

If two angles form a linear pair, then they are supplementary

Vertical angles are congruent