### Substitution Property

If two quantities are equal, then you may replace one with the other in an expression or equation

### Angle Bisector Theorem

If BX(arrow pointing >) is the bisector of Angle ABC, then mAngle ABX=1/2 mAngle ABC and mAngle XBC = 1/2 mAngle ABC

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Theorem 2-4

(Perpendicular Implies Congruence Theorem)

If two lines are perpendicular, then they form congruent adjacent angles

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Theorem 2-5

(Congruence Implies Perpendicular Theorem)

If two lines form congruent adjacent angles, then they are perpendicular

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Theorem 2-6

(Split Perpendicular Theorem)

If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary

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Theorem 2-7

(Supplements of Congruent Angles Theorem)

If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent

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Theorem 2-8

(Complements to Congruent Angles Theorem)

If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent

### Vertical Angle

two angles such that the sides of one angle are opposite rays to the sides of the other angles