Geometric reasoning
Looking for trends, making a conjecture, and verifying the conjecture.

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Undefined termsPoint, line, and airplane.
SegmentConsists of two endpoints and all points that lie on the line in between those endpoints.
RayConsists of an initial allude and all points on the line that lay on either one side of the endallude or the other.
CollinearPoints, segments, or rays that lie on the same line.
AngleTwo various rays that have actually the exact same initial point.
AcuteAn angle whose meacertain is in between 0 and 90 degrees.
RightAn angle whose measure is exactly 90 levels.
ObtuseAn angle whose meacertain is between 90 and 180 levels.
StraightAn angle whose measure is precisely 180 degrees.
ReflexAn angle whose measure is in between 180 and 360 degrees.
InteriorA point that lies in between points that lie on each side of an angle.
ExteriorA suggest that does not lie in the inner of an angle, or on the angle.
AdjacentTwo angles that share a common vertex and also side, however have actually no common interior points.
PostulatesRules in geomeattempt which must be accepted as true without proof; additionally dubbed axioms.
Ruler PostulateThe points on a line have the right to be matched one-to-one through the set of genuine numbers, which enables you to identify the coordinate of a suggest and also the distance in between points.
Segment Addition PostulateIf B is between A and also C, then AB+BC=AC.
Protractor PostulateThe rays that form an angle can be put in one-to-one correspondence through the genuine numbers between 0 and 180 degrees inclusive, which permits angles to be measured.
Angle Addition PostulateAllows you to add the steps of adjacent angles.
CongruentTwo segments or angles having actually the very same measure.
MidpointThe allude that divides a segment into 2 congruent segments.
Segment bisectorA segment, ray, line, or plane that intersects a segment at its midallude.
Angle bisectorA ray that divides an angle right into 2 congruent angles.
PerpendicularTwo lines that intersect to create a right angle.
Distance formulaA formula provided to calculate the distance between two points in a coordinate aircraft.
HypothesisIn a conditional statement, the part complying with the "if" dedetailed by "p".
ConclusionIn a conditional statement, the part complying with the "then" delisted by "q".
Conditional statementA logical statement that can be composed in "if-then" develop.
ConverseA conditional statement formed by interchanging the hypothesis and conclusion.
CounterexampleOne example provided to demonstrate that a conditional statement is false.
Biconditional statementA true conditional statement whose converse is also true.
ReflexiveAny geometric object is congruent to itself.
SymmetricIf one geometric object is congruent to a 2nd, then the second is congruent to the initially.
TransitiveIf one geometric object is congruent to a second, and the second is congruent to a third, then the first object is congruent to the 3rd object.
Vertical anglesTwo angles whose sides create 2 pairs of oppowebsite rays.
Linear pairTwo nearby angles whose nonwidespread sides are opposite rays.
ComplementaryTwo angles whose procedures sum to 90 levels.
SupplementaryTwo angles whose actions amount to 180 degrees.
Liclose to Pair PostulateIf 2 angles develop a linear pair, then they are supplementary.
Vertical Angles TheoremIf two angles are vertical angles, then they are congruent.
Congruent Supplements TheoremIf two angles are supplementary to the same angle or to congruent angles, then they are congruent.
Congruent Complements TheoremIf two angles are complementary to the very same angle or to congruent angles, then they are congruent.

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Deductive reasoningTo factor from recognized facts; offered once proving a theorem.