Postulates
Terms
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- Angle bisector postulate
- An angles has exactly one bisector
- Theorem
- A mathematical statement or proposition that is derived from previously accepted results. Theorems are based on postulates, definitions, or on other established theorems.
- Perpendicular Line Postulate
- Through a point outside a line, there is exactly one line perpendicular to the given line
- Transitive property of equality
- If a = b and b =c then a = c
- Angle addition postulate
- The measures of the angles formed by two adjacent angles is the sum of the measures of these two angles
- Parallel Line postulate
- Through a point outside a line, there is exactly one line parallel to the given line
- Corollary
- A theorem that follows easily from another theorem that has already been proved
- Commutative property of multiplication
- ab = ba
- Substitution property of equality
- If a = b then either a or b may be substituted for other in any equation
- Point at intersection postulate
- Two lines intersect in exactly one point
- Associative property of addition
- (a + b) + c = a + (b + c)
- Point at midpoint postulate
- A segment has exactly one midpoint
- Division property of equality
- If a = b and c does not equal 0 than a/c = b/c
- Addition Property of equality
- If a = b and c = d, then a + c = b +d
- Associative property of multiplication
- (ab)c = a(bc)
- Distributive property
- a(b + c) = ab + ac
- Reflexive property of equality
- a = a
- Segment addition postulate
- If B is between A and C, then AB + BC = AC
- Perpendicular postulate
- The perpendicular segment from a point to a line is the shortest segment from the point to the line
- Commutative property of addition
- a + b = b + a
- Subtraction property of equality
- If a = b and c = d then a - c = b - d
- Multiplication property of equality
- If a = b then ca = cb