Why doesn't Lara just destroy the one she has, rendering the second piece useless?

Lara's whole goal in the film is to destroy the triangle so the Illuminati can't use its evil power. However, after successfully getting the first half at the first tomb, she spends the entire third act trying to acquire the second half in order to destroy them both. The problem is that she has one piece already and one half can not work without joining it with the other.

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