Proof in Geometry

If <1 and <2 are complementary, then m<1 + m<2 = 90

• Addition POE
• Subtraction POE
• Def of right angle
• Def of Complementary Angles

If X is between R & T on a line,
then RX + XT = RT

• Addition POE
• Substitution POE
• Angle Addition Post.
• Segment Addition Post.

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

Given: segment AM is congruent to segment MB

Prove: M is the midpoint of segment AB

• Definition of Midpoint

• Definition of Segment Bisector

• Definition of Congruent Segments

• Segment Addition Posulate

Given: Ray BD bisects <ABC.
Prove: m<ABC=m<DBC

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

Given: the picture
Prove: m<AOB+m<BOC=m<AOC

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

m∠4 = m∠4

• Substitution Property of Equality

• Reflexive Property of Equality

• Symmetric Property of Equality

• Transitive Property of Equality

If m∠1 = m∠2 and m∠2 = m∠3, then m∠1 = m∠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