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Level 137

Postulates, Definitions & Theorems for Proofs


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Segment Addition Postulate
If A, B, and C are collinear, then point B is between A and C if and only if AB + BC = AC.
Angle Addition Postulate
D is in the interior of angle ABC and only if m<ABD + m<DBC = m<ABC.
Def. of Congruent Segments
Two segments are congruent if and only if they have the same measure
Def. of Congruent Angles
2 angles are congruent if and only if they are equal
Def. of Midpoint
a point is a midpoint if and only if it divides a segment into 2 congruent segments
Def. of Complementary Angles
∠A and ∠B are complementary if and only if m∠A + m∠B = 90°
Def. of Supplementary Angles
∠A and ∠B are supplementary if and only if m∠A + m∠B = 180°
Def. of a Right Angle
∠A is a right angle if and only if m∠A = 90°
Supplement Theorem
If two angles form a linear pair, then they are supplementary angles.
Complement Theorem
If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles.
Vertical angles theorem
If two angles are vertical angles, then they are congruent.