2-Column Proofs

converse of a conditional statement (is it true or not)

-When the hypothesis and conclusion are switched. The converse of p ➝ q is q ➝ p. -A statement formed by interchanging the hypothesis and the conclusion in a conditional statement. -Only true if it is true all the time

transitive property

Two things equal to the same thing are equal to each other. In other words, if we know that a = b and that b =c, then we can conclude that a = c. Could be used for numbers or segments/angles.

Can you use the definition of a term (ex. midpoint/congruency/right angle) as a step?

Yes, a reason can be a property, definition, postulate, or theorem (not using right now).

distributive property

a(b + c) = ab + ac, could be used for numbers or segments/angles

bisector

angle: an angle bisector is a ray, segment, or line divides an angle into two congruent angles (show with arc marks). segment: a ray, segment, or line that intersects a segment at its midpoint

reflexive property

any # is equal to itself, a = a

division property

both sides of an equation can be divided by the same quantity

multiplication property

both sides of an equation can be multiplied by the same quantity

angle addition postulate

for any angle, the measure of the whole is equal to the sum of the measures of its parts

conclusion

the part of a conditional statement following the word then

subtraction property

the same quantity can be subtracted from both sides of an equation

symmetric property

we can switch the expressions of the left and right sides of an equation that is if we know that a= b, then we can conclude that b=a, could be use for numbers or segmebts/angles

Some problems will not give you #'s so know your definitions

1. Right angle: angle that equals 90 degrees 2. Perpendicular: two lines that make a right angle 3. Congruency (use whenever you are trying to change equal sign to congruent sign), measures of angles that are equal are congruent

conditional statement

A logical statement that has two parts, a hypothesis and a conclusion

midpoint

A point that divides a segment into two congruent segments

segment addition postulate

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

substitution property

If a=b, then b can replace a in any expression (any time you are plugging things in, don't confuse with transitive-remember transitive train)

Not really a property/postulate but.... given

The first step of every 2-column proof, just what you are already given from the problem.

hypothesis

The part of a conditional statement following the word if