Geometry definitions
Terms
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- transitive property of congruence
- a ~= b and b ~= c then a ~= c
- segment bisector
- a line, ray, segment or plane that intersects at its midpoint
- pythagorem theorem
- a² + b² = c²
- p --> q
- conditional statement
- multiplication property
- if a = b then a x c = b x c
- subtraction property
- if a = b then a - c = b - c
- supplementary angles
- two angles whose sum is 180°
- linear pair
- two adjacent angles whos non-common sides form a pair of opposite rays
- division property
- if a = b and c ≠ 0 then a/c = b/c
- substitution property
- if a = b then a may be replaced by b in any equation or expression
- ruler postulate
- for any two points on a line, the length or the segment containing those two points is the absolute value of the difference of the coordinates of the points
- ray
- part of a line that has an intial point and extends forever in one direction
- counterexample
- show that a conditional statement is false
- congruent supplements theorem
- if two angles are supplementary to the same angle or to two congruent angles then they are congruent
- ~q --> ~p
- contrapositive
- congruent complements theorem
- if two angles are complementary to the same angle or to 2 ~= angles, then they are congruent
- proof
- a logical argument with evidence to support your statement
- transitive property of equality
- if a = b and b =c, then a = c
- vertical angles
- two non-adjacent angles that are formed when two lines intersect
- skew lines
- two non collinear lines not on the same plane that are not parallel and will never intersect
- inverse
- when you negate (write the opposite/negative of) the hypothesis and the conclusion of the conditional statement
- converse
- switching the hypothesis and the conclusion of the original conditional statement
- ^
- and
- distribution property
- a(b+c) = ab + ac
- parallel
- two coplanar lines or planes that never intersect
- perpendicular
- two coplanar lines or two planes that intersect and form a right angle
- adjacent angles
- two angles in the same plane that have a common vertex and common side but no common interior points
- biconditional statement
- a statement that uses "if and only if"
- acute angle
- greater than O° but less than 90°
- ~p --> ~q
- inverse
- complementary angles
- two angles whos sum is 90°
- addition property
- if a = b, then a + c = b + c
- coplanar
- three or more noncollinear points that lie on the same plane
- reflexive property of congruence
- a ~= a
- symmetric property of congruence
- a ~= b then b ~= a
- vertical angle theorem
- if two angles are vertical angles then they are congruent
- q
- conclusion
- reflexive property of equality
- a = a
- conjectures
- an educated guess
- right angle
- 90°
- straight angle
- 180°
- collinear
- three or more points that lie on the same line
- congruent
- same size, same shape
- linear pair postulate
- if two angles form a linear pair, then they are supplementary
- obtuse angle
- greater than 90° but less than 180°
- congruent angles
- two angles that have the same measure
- contrapositive
- when you switch the hypothesis and the conclusion and negate the hypothesis and conclusion of the original statement
- q --> p
- converse
- conditional statement
- a statement in if-then form
- perpendicular bisector
- a segment bisector that forms a 90° angle with the original segment
- segment
- part of a line with a definite beginning and definite endpoint
- V
- or
- segment addition postulate
- if B is between two points (A and C) then AB + BC = AC
- p <--> q, q <--> p
- biconditional
- symmetric property of equality
- if a = b, then b = a
- midpoint
- a point on a segment that divides the segment into two congruent segments
- angle
- two rays with the same intial point that are not coinciding
- p
- hypothesis
- inductive reasoning
- looking a several examples and making a conjection
- angle bisector
- a ray that divides an angle into two congruent angles
- angle addition postulate
-
if a point P is in the interior of an angle,
- opposite rays
- two rays with the same intial point that form a straight line