Proofs Using Angle Properties

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

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

∠4 = ∠4

• Substitution Property of Equality
• Reflexive Property of Equality
• Symmetric Property of Equality
• Transitive Property of Equality

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 ∠CAT is a right angle, then m∠CAT = 90°.

• Definition of Right Angle
• Definition of Congruent Angles
• Angle Addition Postulate
• Segment Addition Postulate

If AC ⟂ BD, then ∠DBC is a right angle.

• Definition of Perpendicular Lines
• Definition of Right Angle
• Angle Addition Postulate
• Segment Addition Postulate

If DB bisects ∠ABC, then ∠ABD = ∠CBD.

• Definition of Congruent Angles
• Definition of Angle Bisector
• Angle Addition Postulate
• Definition of Right Angle

If ∠DOG = ∠DOG, then m∠DOG ≅ m∠DOG.

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