Honors Geometry Companion Book, Volume 1

2.2.1 Algebraic Proof (continued)

The statement 80° = 80° shows that a degree measurement is equal to itself. The Reflexive Property of Equality states that a = a , or that any number a is equal to itself. So, the Reflexive Property of Equality justifies the statement. The second statement shows that one segment is congruent to another, so the second segment is congruent to the first. The Symmetric Property of Congruence states that if a figure is congruent to a second figure, then it must be true that the second figure is congruent to the first figure. So, the statement is justified by the Symmetric Property of Congruence. The third statement shows that an angle is congruent to itself. This appears to be the same property as the first statement. However, notice that congruency is used here, not equality. Therefore, the Reflexive Property of Congruence justifies this statement. In the third statement, the relationship between three congruent segments is described. Generally speaking, this statement shows that if segment 1 is congruent to segment 2 and segment 2 is congruent to segment 3, then segment 1 is congruent to segment 3. This is an example of the Transitive Property of Congruence.


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