Lines Postulates And Theorems Name Definition Visual Clue Segment Addition For any segment, the measure of the whole postulate is equal to the sum of the measures of its non-overlapping parts Postulate Through any two points there is exactly one line Postulate Common Segments Theorem If two lines intersect, then they intersect at exactly one point. Interior of an angle is Angle Bisector equidistant from the sides of the angle, then Theorem it is on the bisector of the angle. Angle Bisector If a point is on the bisector of an angle, then Theorem it is equidistant from the sides of the angle. Congruence Theorem Vertical Angles Vertical angles are equal in measure Theorem Theorem If two congruent angles are supplementary, then each is a right angle. theorem Right Angle All right angles are congruent.
Congruent If two angles are complements of the same complements angle, then they are congruent. Congruent If two angles are supplements of the same supplements theorem angle, then they are congruent. If a = b and b = c then a = c a(b + c) = ab + acĬongruence Postulates Name Definition Reflexive Property of Congruence A ≅ A Symmetric Property of If A ≅ B, then B ≅ A Congruence Transitive Property of Congruence If A ≅ B and B ≅ C then A≅C of 11Īngle Postulates And Theorems Name Definition Angle Addition For any angle, the measure of the whole is postulate equal to the sum of the measures of its nonoverlapping parts Linear Pair Theorem If two angles form a linear pair, then they are supplementary. Of equality Transitive Property of Equality Distributive Propertyĭefinition If the same number is added to equal numbers, then the sums are equal If the same number is subtracted from equal numbers, then the differences are equal If equal numbers are multiplied by the same number, then the products are equal If equal numbers are divided by the same number, then the quotients are equal A number is equal to itself If a = b then b = a If values are equal, then one value may be substituted for the other. Of equality Symmetric Property of Equality Substitution Prop.
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