Geometric reasoning
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Looking for patterns, do a conjecture, and verifying the conjecture.

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Undefined termsPoint, line, and plane.
SegmentConsists of 2 endpoints and also all points that lie top top the line between those endpoints.
RayConsists of an initial allude and every points top top the line that lay on either one side of the endpoint or the other.
CollinearPoints, segments, or rays the lie top top the exact same line.
AngleTwo different rays that have actually the same initial point.
AcuteAn edge whose measure is in between 0 and also 90 degrees.
RightAn edge whose measure is precisely 90 degrees.
ObtuseAn edge whose measure up is in between 90 and 180 degrees.
StraightAn edge whose measure is exactly 180 degrees.
ReflexAn edge whose measure up is in between 180 and also 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 angle that share a typical vertex and also side, however have no usual interior points.
PostulatesRules in geometry which should be embraced as true without proof; likewise called axioms.
Ruler PostulateThe point out on a line deserve to be matched one-to-one v the set of genuine numbers, which permits you to recognize the name: coordinates of a point and the distance between points.
Segment enhancement PostulateIf B is in between A and also C, climate AB+BC=AC.
Protractor PostulateThe rays that form an angle have the right to be placed in one-to-one correspondence v the genuine numbers in between 0 and 180 levels inclusive, which permits angles to be measured.
Angle enhancement PostulateAllows friend to include the steps of nearby angles.
CongruentTwo segments or angles having the exact same measure.
MidpointThe allude that divides a segment into two congruent segments.
Segment bisectorA segment, ray, line, or airplane that intersects a segment at its midpoint.
Angle bisectorA beam that divides one angle right into two congruent angles.
PerpendicularTwo lines that crossing to type a right angle.
Distance formulaA formula used to calculate the distance in between two clues in a coordinate plane.
HypothesisIn a conditional statement, the component following the "if" denoted by "p".
ConclusionIn a conditional statement, the component following the "then" denoted by "q".
Conditional statementA logical statement that deserve to be composed in "if-then" form.
ConverseA conditional statement created by interchanging the hypothesis and also conclusion.
CounterexampleOne example used to demonstrate that a conditional statement is false.
Biconditional statementA true conditional statement whose converse is likewise true.
ReflexiveAny geometric thing is congruent to itself.
SymmetricIf one geometric thing is congruent to a second, climate the second is congruent to the first.
TransitiveIf one geometric thing is congruent to a second, and the 2nd is congruent to a third, climate the first object is congruent to the third object.
Vertical anglesTwo angle whose sides form two bag of opposite rays.
Linear pairTwo nearby angles whose noncommon sides room opposite rays.
ComplementaryTwo angle whose steps sum come 90 degrees.
SupplementaryTwo angles whose actions sum come 180 degrees.
Linear Pair PostulateIf 2 angles type a direct pair, climate they space supplementary.
Vertical angle TheoremIf 2 angles are vertical angles, climate they space congruent.
Congruent additional TheoremIf 2 angles space supplementary to the same angle or to congruent angles, then they room congruent.
Congruent Complements TheoremIf two angles are complementary come the same angle or come congruent angles, climate they room congruent.

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Deductive reasoningTo reason from recognized facts; provided when proving a theorem.
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