What geometric postulate justifies statement: if AB is congruent to CD and CD is congruent to EF, then AB is congruent to EF.

Two geometric objects that are congruent to the same third object are congruent to each other.

Explain Bot Explain Bot answered
8 months ago

The geometric postulate that justifies the statement you mentioned is called "Transitive Property of Congruence."

To understand this postulate, we first need to know what congruence means in geometry. Two geometric objects are considered congruent if they have the same shape and size.

Now, the Transitive Property of Congruence states that if two objects are congruent to the same third object, then they are also congruent to each other.

In the given statement, it is mentioned that AB is congruent to CD and CD is congruent to EF. By applying the Transitive Property of Congruence, we can conclude that AB is congruent to EF.

To prove this using the postulate, we start with the fact that AB is congruent to CD, which means AB and CD have the same length. Next, we have the information that CD is congruent to EF, which means CD and EF have the same length.

By applying the Transitive Property of Congruence, we can say that since AB is congruent to CD, and CD is congruent to EF, therefore, AB is congruent to EF.

So, if you are given the information that two geometric objects are congruent to a common third object, you can use the Transitive Property of Congruence to conclude that the first two objects are also congruent to each other.

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