Geometry Review

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

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

What is the justification?

• Symmetric Prop.
• Angle addition postulate
• Reflexive Prop
• Transitive Prop.

What is the justification?

• Symmetric Prop.
• Angle addition postulate
• Reflexive Prop
• Transitive Prop.

What is the justification?

• Reflexive Prop.
• Symmetric Prop.
• Transitive Prop.
• Substitution

State the proof reason given:

angle 2 & angle 4 are supplementary

• Same side interior angle theorem

• Same side exterior angle theorem

• Definition of supplementary

• Linear Pair Postulate

What is the reason for the  statements above?

• Definition of Congruence
• Symmetric Property of Congruence
• Reflexive Property of Equality
• Congruent Segments Theorem