FoG 2.3 Congruent Segments

This unit defines congruent segments, gives the properties of congruency and gives formulas for midpoints in 1 dimension.

1. Congruent Segments Section 2.3

2. Two segments are congruent if and only if they have the same length. Below AB ≅ CD (“≅” means “is congruent to”) Congruent Segments A B C D 2 cm 2 cm

3. Theorems are statements derived by logical argument using definitions and accepted facts. Primary Theorems of segments Theorems of Segments Congruence of Segments is: Meaning: Reflexive AB ≅ AB Symmetric If AB ≅ CD, then CD ≅ AB Transitive If AB ≅ CD & CD ≅ EF, then AB ≅ EF

4. A Midpoint is the point that is the same distance from each endpoint For a segment with endpoints A an B, it is found using the formula: M = ½ ( A + B ) Midpoint A M B

5. Length AB = ∣ B – A ∣ Midpoint length formulas AM = MB AM = ½ AB MB = ½ AB Formulas for Segments A M B