Show that ∼= is an equivalence relation for congruent segment by show the three properties hold, ...
Show that ∼= is an equivalence relation for congruent segment by show the three properties hold, reflexive, symmetric, and transitive.
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(Transitive Property) If AB ∼= CD and CD ∼= EF then AB ∼= EF.
Homework Answers
A line segment is congruent to itself. So ~= is reflexive.
Let AB~=CD.So both AB and CD have same lengths. So CD~=AB. Hence ~= is Symmetric.
Now let AB~=CD and CD~=EF. This means AB and CD have same lengths and CD and EF have same lengths. This means that all the three line segments AB, CD and EF have same length. In particular, AB and EF have same lengths. That is, AB~=EF.
So ~= is transitive. Hence ~= is equivalence relation.
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Show that ∼= is an equivalence relation for congruent segment by show the three properties hold, ...
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