Vocabulary
Conditionals
Random Special Category
Theorems and Postulates
5.1
100
Statement that can be written in the form "if p, then q"
What is a conditional statement
100
Hypothesis: today is thanksgiving day Conclusion: today is Thursday
What is the hypothesis and conclusion of the conditional statement "if today is thanksgiving day, then today is Thursday"
100
Arriving at a conclusion based on observations.
What is inductive reasoning?
100
Linear pair theorem?
If 2 angles form a linear pair, then they are supplementary
100
What is a locus?
What is A set of points that justifies a given condition
200
A statement that can be written in the form "p if and only if q"
What is a biconditional statement
200
What is the hypothesis and conclusion of the conditional statement " a number is a rational number, if it is an integer"
Hypothesis: a number is an integer Conclusion: the number is a rational number
200
To arrive at a conclusion using facts, definitions, rules, or properties.
What is deductive reasoning?
200
What is the congruent supplements theorem?
If 2 angles are supplementary to the same angle (or 2 congruent angles), then the 2 angles are congruent
200
What is the converse of perpendicular bisector theorem?
If a point is equidistant from the end points of a segment, then it is on the perpendicular Bisector of the segment
300
The statement formed by both negating and exchanging the
What is a contrapositive statement
300
What is a conditional statement that can be written from "an acute triangle angel has all acute angles"
"If a triangle is an acute triangle, then it has all acute sides"
300
Solve this equation and justify each step/ 5+x=2x
5+x=2x -given -x=-x - subtraction POE 5=x - division
300
What is the right angle congruence theorem?
All right angles are congruent
300
What is the angle bisector theorem?
If a point is on the bisector of angle, then it is equidistant from the sides of the angle
400
Using algebraic properties to show a conclusion is true
What is an algebraic proof
400
Is this a correct biconditional statement? If not make a correct one: "If an orange is fruit, then it is healthy"
No; this is not a true biconditional because the converse and inverse of this conditional statement are not true.
400
Is (a x b) x c the same as (c x b) x a? What reasoning would you use to solve this?
Yes, it is the same. Ding deductive reasoning.
400
If 2 angles are complementary to the same angle (or 2 congruent angles) then the 2 angles are congruent.
What is the congruent compliments theorem?
400
The same distance from 2 or more objects
What is equidistant?
500
What is the converse, inverse, and contrapositive of this statement: "If you are happy, then you are smiling". What is the truth value in this statement?
Converse: "If you are smiling, then you are happy" Inverse: "if you are not smiling, then you are not happy" Contrapositive:"if you are not happy, then you are not smiling" This statement is true
500
Write a 2 column proof for the following: <1 and <2 are supplementary and <2 and <3 are supplementary. Prove <1 is congruent to <3
See board
500
Which theorem is needed for the following question? Angle a compliments angle b. Angle b measures 30 degrees. Angle c is a compliment to angle b. What is the measure of angle c?
What is the congruent compliments theorem?
500
Write an equation for the perpendicular bisector of the segment with endpoints P(5,2) and Q(1,-4) in point slope form You will need to graph this
Y-1=-2/3+(x-3)
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