ASN
Determine whether this statement is sometimes, always, or never true: The intersection of two planes contains at least two points.
Always
Which postulate is used to show that two smaller segments add to one large segment?
Segment Addition Postulate
Vertical Angles Theorem
What is another name for a postulate?
Axiom
Complete the missing part of this proof (statements are numbered and reasons are in parentheses): 1. angle 1 and angle 2 are vertical (given). 2. <1 is congruent to <2 (????????)
Vertical Angles Theorem
Determine whether this statement is sometimes, always, or never true: three points create a plane.
Sometimes. If the points are collinear, they will create only a line and not a plane.
The intersection of two lines is a ___________ .
Plane
This theorem explains the relationship between angles of a linear pair. What is that relationship?
Supplementary. They add to 180 degrees.
What is the name of the statement that immediately comes after the word "then" in an if-then statement?
Conclusion. The "if" part is the hypothesis. This whole statement is called a conditional statement.
Complete the missing part of this proof (statements are numbered and reasons are in parentheses): 1. B is the midpoint of AC (given). 2. AB = BC (???????)
Midpoint Theorem
Determine whether this statement is sometimes, always, or never true: Points X and Y are in plane P. Any point collinear with X and Y will also be in plane P.
Always. If two points lie in a plane, then the entire line containing those points also lies in that plane. So if a point is collinear, then it is on the line XY and also in plane P.
Which postulate shows that two smaller angles add to one large angle?
Angle Addition Postulate
This theorem describes the relationship between complementary angles. What do we know about complementary angles?
They add to 90 degrees.
What is the name for a mathematical statement that has been proven?
Theorem
What reason do you use for converting an equation from congruent to equal?
Definition of congruence
Determine whether the statement is sometimes, always, or never true: There are two unique lines through points A and B.
Never. Through any two points there is exactly one line.
A plane is made of at least _____ _____________ points.
3 non-collinear
What does it mean for lines to be perpendicular?
They form four right angles.
To show that a conjecture is false, you must find a _____________ .
Counterexample. It only takes one counterexample to prove a statement FALSE.
Complete the missing part of this proof (statements are numbered and reasons are in parentheses): 1. AB = CD (given) 2. BC = BC (reflexive POE) 3. AB + BC = CD + BC (???????????)
Addition POE. This is because BC was added to both sides of the equation.
Determine whether the statement is sometimes, always, or never true: Any two lines will intersect.
Sometimes. They will intersect as long as they aren't parallel.
If two points lie in a plane, what do you know about the line that connects them?
The entire line is also in the plane.
Which theorem is used when a segment is cut in half to show two congruent smaller segments?
Midpoint Theorem
What is the name of a mathematical statement that is accepted as true without proof?
Postulate
Complete the missing part of this proof (statements are numbered and reasons are in parentheses): 1. AB = BC and BC = CD (given) 2. AB = CD (?????????)
Transitive POE. If AB = BC and BC = CD, then AB = CD (chain).