the sketch of if AM is not = MY, then M is not the midpoint of segment AY.
To prove the statement "If AM is not equal to MY, then M is not the midpoint of segment AY," we can use a proof by contradiction. Let's break down the steps to prove this statement:
1. Assume that AM is not equal to MY.
- This is our assumption or hypothesis that we will use to prove the statement false.
2. Assume that M is the midpoint of segment AY.
- This is the opposite of what we're trying to prove, so we will assume it to be true initially.
3. Since M is the midpoint of segment AY, we can say that AM is equal to MY.
- By definition, a midpoint divides a segment into two equal parts.
4. However, our assumption in step 1 states that AM is not equal to MY.
- This contradicts step 3, where we assumed M to be the midpoint of segment AY.
5. Therefore, our initial assumption in step 2 that M is the midpoint of segment AY must be false.
- If our assumption leads to a contradiction, then it cannot be true.
6. Since M is not the midpoint of segment AY, we can conclude that if AM is not equal to MY, then M is not the midpoint of segment AY.
In summary, we have proven the statement "If AM is not equal to MY, then M is not the midpoint of segment AY" by contradiction.