Line Segment and Angle Proofs

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 ∠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

What reason supports the statement?

• Vertical angles are congruent.

• Parallel implies alternate interior angles are congruent.

• Parallel implies corresponding angles are congruent.

• Reflexive Property

What reason supports the statement?

• Parallel implies alternate interior angles are congruent.

• Parallel implies corresponding angles are congruent.

• Vertical angles are congruent.

• Reflexive Property

Why is ∠KJM ≌∠LMJ?

• Alternate Exterior angles are congruent

• Alternate Interior Angles are congruent

• Corresponding Angles are Congruent

• Consecutive Interior angles are supplementary

Why is ∠KMJ ≌∠LJM?

• Alternate Exterior angles are congruent

• Alternate Interior Angles are congruent

• Corresponding Angles are Congruent

• Consecutive Interior angles are supplementary

What is the justification (reason)?

• reflexive property

• definition of segment bisect

• definition of a midpoint

• substitution property

What should the reasons be for the first 2 statements?

• Reflexive

• Side Side Side

• Alternate Interior Angles

• Given