1. Proofs

2. Definitions
Definition of Congruence – two figures are congruent if and only if one can be obtained from the other by a sequence of rigid motions (reflections, translations, and/or rotations)

3. Definition
Corresponding Parts of Congruent Figures are Congruent – if two figures are congruent, then corresponding sides are congruent and corresponding angles are congruent

4. Definition
Segment Bisector – any line, segment, ray, or point (midpoint) that splits a segment into two congruent segments (splits a segment in half)
Midpoint – a point that splits a segment into two congruent segments (splits a segment in half)
Angle Bisector – (review) any line, segment, or ray that splits an angle into two congruent angles (splits an angle in half)

5. Notation for denoting congruence:

6. Properties of Congruence

7. CPCFC
Given
Transitive Property

8. CPCFC Given Transitive Property
1. Quadrilateral ABCD ≅ Quadrilateral EFGH
2. Segment AD ≅ Segment CD
3. Segment CD ≅ Segment GH
4. Segment AD ≅ Segment GH
CPCFC
Given
Transitive Property

9. Definition of an Angle Bisector
1. Triangle MQN ≅ Triangle MQP
2. ∠NMQ ≅ ∠PMQ
3. Segment MQ bisects ∠NMP
CPCFC
Given
Definition of an Angle Bisector