Giving Reasons for Proofs About Angles

A line or line segment that divides an angle into two equal parts

• Bisector
• Complementary

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 ∠BAT and ∠MAN are vertical angles,
then ∠BAT ≅ ∠MAN.

• Vertical Angles Theorem
• Definition of Congruent Angles
• Angle Addition Postulate

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

State the reason, given:

If B is the midpoint of RL, then RB=BL

• Definition of congruent segments

• Segment addition postulate

• Given

• Definition of midpoint