Congruent line segments

Key Notes :

Two segments are congruent (≅) if they have the same length.

Introduction:

• Definition of Congruence: In geometry, the term “congruence” indicates that two geometric figures are identical in shape and size. When it comes to line segments, congruence implies that two segments have the same length.
• Congruent Line Segments: Line segments are congruent if they have equal lengths. This concept is fundamental in geometry and plays a crucial role in various geometric proofs and constructions.

Properties of Congruent Line Segments:

1. Equal Lengths:
   • The most fundamental property of congruent line segments is that they have the same length.
   • If AB and CD are congruent line segments, then the measure of AB is equal to the measure of CD.
2. Symbolic Representation:
   • Congruent line segments are often denoted using the symbol ≅.
   • For example, if AB≅CD, it signifies that line segments AB and CD are congruent.

Methods of Proving Congruent Line Segments:

1. Measurement:
   • Direct measurement using a ruler is the simplest way to show that two line segments are congruent.
2. Congruence Postulates:
   • Side-Side-Side (SSS) Congruence Postulate: If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent.
   • Side-Angle-Side (SAS) Congruence Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent.

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