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