Proofs: What is the reason?

If B is the midpoint of AC, then AB ≅ BC.

• Definition of Congruent Segments

• Definition of Midpoint

• Vertical Angles Theorem

• Definition of Angle Bisector

Which postulate or definition states that
m∠ADB + m∠BDC = m∠ADC?

• Segment Addition Postulate

• Angle Addition Postulate

• Definition of Angle Bisector

• Definition of Congruent Angles

If ∠A and ∠B are complementary,
then m∠A + m∠B = 90°.

• Definition of Supplementary Angles

• Angle Addition Postulate

• Definition of Right Angle

• Definition of Complementary Angles

If ∠1 and ∠2 are supplementary,
then m∠1 + m∠2 = 180°.

• Definition of Supplementary Angles

• Angle Addition Postulate

• Vertical Angles Theorem

• Definition of Complementary Angles

If ∠1 = ∠2 and ∠2 = ∠3, then ∠1 = ∠3.

• Addition Property of Equality

• Symmetric Property of Equality

• Reflexive Property of Equality

• Transitive Property of Equality

If DB bisects ∠ABC, then ∠ABD = ∠CBD.

• Definition of Congruent Angles

• Definition of Angle Bisector

• Angle Addition Postulate

• Definition of Right Angle

State the proof reason, given: If AB=BC and BC=CD, then AB=CD

• Segment Addition Postulate

• Transitive Property

• Reflexive Property

• Subtraction Property of Equality

What reasons supports the statement?

• Symmetry Property

• Reflexive Property

• Transitive Property

• SSS

What reason supports the statement?

• Vertical angles are congruent.

• Parallel implies alternate interior angles are congruent.

• Parallel implies corresponding angles are congruent.

• Reflexive Property

Given that angles A and B form a linear pair what is the next step we can conclude by definition of a linear pair?

• m∠A + m∠B = 90

• A and B are both acute angles

• m∠A + m∠B = 180

• A and B are both obtuse angles