Geometry

Question Analysis：
This question involves using proof by contradiction in the context of the triangle inequality theorem.
The main focus is setting up the negation of the conclusion to begin a contradiction.

Key Concept Explanation：
In contradiction proofs, we assume that the conclusion is false and try to derive an impossibility.
Here, the statement is:
"If side lengths are 7, 10, and x, then x < 17"
So we assume:
x ≥ 17
Then use triangle inequality:
Sum of any two sides > the third

Step-by-Step Solution：
Assume x ≥ 17
Triangle has sides 7, 10, and x
Use triangle inequality:
7 + 10 = 17
7 + 10 > x → contradiction if x ≥ 17
Therefore, x must be < 17

Option Analysis：
A. ❌ x = 17 is only one case; doesn’t cover all contradictions
B. ❌ This is what we want to prove, not assume
C. ✅ Correct assumption: negation of the conclusion
D. ❌ Arb...