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What are some tips for geometry proof practice?

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Quick Answer

Some tips for geometry proof practice are to break the problem down into smaller pieces, to label all necessary points, lines and planes and to write down the reasoning for each step. Another tip is to understand the proper use of examples in a mathematical proof.

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Full Answer

When students don't know how to begin a proof, tackling a smaller task sometimes helps. The student should divide the proof into different sections and work on one at a time. For example, when a student is trying to prove that two triangles are congruent, they could begin by proving that an angle of one triangle is equal to an angle of the other triangle. They could then proceed to prove that a side of one triangle has the same length as the corresponding side of the other triangle.

Labeling geometric objects before beginning the proof is important to avoid confusion. The student should use a consistent labeling system, such as labeling points with lowercase letters starting with "a," "b" and "c."

Writing down the justification for each step of the proof helps the student avoid leaps of logic. Some geometry teachers require students to note their reasoning in a separate column. Alternatively, the student could write axioms and theorems on index cards and lay the cards out in the order those ideas appear in the proof.

Many students struggle to use examples appropriately in geometry proofs. A good rule to remember is that giving an example does not prove a statement true. However, if the student is trying to show a statement to be false, a single counterexample is usually enough of a proof.

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