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