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Section 2.3
Two segments are congruent if and only if they have the same length.
Below AB ≅ CD (“≅” means “is congruent to”)
A
B C
D
2 cm 2 cm
Theorems are statements derived by logical argument using definitions and accepted facts.
Primary Theorems of segments
Congruence of Segments is: Meaning:
Reflexive AB ≅ AB
Symmetric If AB ≅ CD, then CD ≅ AB
TransitiveIf AB ≅ CD & CD ≅ EF,
then AB ≅ EF
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 )
A
M
B
Length
AB = ∣ B – A ∣
Midpoint length formulas
AM = MB
AM = ½ AB
MB = ½ AB
A
M
B