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Welcome! Today we are going to learn how to write a geometry proof, which is just like building a logical path to a treasure!
In geometry, a proof is a step-by-step explanation that shows why a statement must always be true. We start with facts we already know (called Givens) and use logical steps to reach our final destination.
Think of a proof like a chain of dominoes. When the first domino falls (the Given), it knocks over the next one (a logical definition or theorem), until the very last one falls (our Prove statement).
Every single step in our proof must have a 'Reason' to back it up. We use definitions, postulates, or theorems we've already learned to justify our statements.
Given that Point M is the midpoint of line segment AB, prove that the length AM is equal to the length MB.
- Identify the Given statement: 'M is the midpoint of AB'.
- Write down the definition of a midpoint: A midpoint divides a segment into two equal parts.
- State your claim: Segment AM is congruent to segment MB.
- Provide the reason: 'Definition of midpoint'.
- Conclude that the lengths AM = MB because congruent segments have equal lengths.
