Congruency of Line Segments
Line segments have only one dimension - length. Two line segments are congruent if and only if they have the same length.
When we write AB ≅ CD, it means line segment AB is congruent to line segment CD
Notation: The symbol "≅" represents
Fundamental Properties
Reflexive Property
Every line segment is congruent to itself AB ≅ AB
Symmetric Property
If AB ≅ CD, then CD ≅ AB Congruency works both ways
Transitive Property
If AB ≅ CD and CD ≅ EF, then AB ≅ EF Congruency carries forward
Examples of Congruent Line Segments
Ex 1
A•—————————————•B
C•—————————————•D
These line segments are
Both have the same
If we trace AB and place it on CD, they match perfectly
We write this as AB ≅ CD
Ex 2
P•——————•Q
R•———————————•S
These line segments are
They have different lengths If we trace PQ and place it on RS, they won't match
Ex 3
A•————•B
| |
D•————•C
All sides of a square are
AB ≅