Properties of Segment Congruence relationships
A true statement that follows as a result of other true statements is called a theorem. All theorems must be proved. You can prove a theorem using a two - column proof. A two - column proot has numbered statements and reasons that show the logical order of a argument.
Theorem |
Theorem : Properties of Segment Congruence
Segment congruence is reflexive, symmetric, and transitive.
Here are some examples: |
REFLEXIVE |
For any segment AB ,  @  . |
SYMMETRIC |
If  @  , then  @  . |
TRANSITIVE |
If  @  , and  @  , then  @  |
Example: Symmetric Property of Segment Congruence
You can prove the Symmetric Property of Segment Congruence as follows.
Given :  @ 
Prove :  @ 
Statements |
Reasons |
1.  |
1. Given |
2. PQ = XY |
2. Definition of congruent segment |
3. XU = PQ |
3. Symmetric property of equality |
4.  |
4. Definition of congruent segements |
A proof can be written in paragraph form, called paragraph proof. Here is a paragraph proof for the Symmetric Property of Segment Congruence.
Paragraph Proof: You are given that  . By the definition of congruent segments. PQ = XY. By the symmetric property of equality, XY = PQ . Therefore, by the definition of congruent segments, if follows that  .
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