Will's WorkBench

• Law of Detachment- if p-->q is a true conditional and p is true then q must be true
• Syllogism- If p-->q and q-->r are true conditionals, then p-->r is also true
• If 2 angles form a linear pair, then the angles are supplementary
• Vertical angles are congruent
• If the non- common side of 2 adjacent acute angles lie on perpindicular lines then the angles are complementary
• All right angles are congruent
• If 2 lines are perpindicular they meet to form congruent adjacent angles
• If 2 lines are perpindicular they meet to form right angles
• If 2 angles are supplements of the same angle or 2 congruent angles, then they are congruent
• If 2 angles are complements of the same angle or congruent angles then they are congruent
• If 2 angles are congruent and supplementary then each is a right angle
• if 2 angles are congruent than the complement of one is the complement of the other
• If 2 angles are formed by joining 2 pairs of congruent adjacent supplementary angles, then the larger angles are congruent
• If 2 angles are both congruent and supplementary then each is a right angle
• If 2 congruent angles form a linear pair, then each angle is a right angle
• If 2 lines intersect to form congruent adjacent angles then the lines are perpindicular

Postulates

1. If a=b then a+c=b+c - Addition POE
2. If a=b then a-c=b-c - Subtraction POE
3. If a=b then ac=bc - Multiplacation POE
4. If a=b and c does not equal 0 then a/c = b/c- Division POE
5. a=a - Reflexive Property
6. If a=b and b=c then a=c - Transitive POE AB + BC= AC and AC = EF + GH then AB + BC = EF + GH - Transitive POE replaces the entire side of an equation.
7. If AB + BC= AC and AB=BC then 2AB=AC - Substitution only replaces part of equation
8. A midpoint separates a segment into 2 smaller segments of equal length - FG=GH
9. AB+BC=AC - Segment Addition Postulate
10. m<1 + m<2 = m<ABC - Angle Addition Postulate
11. m<1 + m<2 = 180 - Angle Addition Postulate Special Case
12. m<1 + m<2 + m<3 = 180 - Extended Angle Addition Postulate Special Case
13. If a segment is bisected then the smaller segments formed are congruent
14. If 2 segments are congruent and each is at its midpoint, then the smaller segments are all congruent to each other
15. If 2 larger segments are formed by joining 2 pairs of equal subsegments then the segment formed are equal
16. transitive and reflexive are properties of congruent of angles and congruent of segments

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