## Geometry: Common Core (15th Edition)

$D$
Let's look at each of the options separately. Option A: Using the Triangle Inequality Theorem, we need to see if the sum of each of the combinations of two sides is greater than the other side: $7 + 10 > 25$ --> This statement is false. $10 + 25 > 7$ --> This statement is true. $7 + 25 > 10$ --> This statement is true. A triangle cannot have these lengths for its sides because two of the sides added together are not greater than the third side. Option B: Using the Triangle Inequality Theorem, we need to see if the sum of each of the combinations of two sides is greater than the other side: $4 + 6 > 10$ --> This statement is false. $6 + 10 > 4$ --> This statement is true. $10 + 4 > 6$ --> This statement is true. A triangle cannot have these lengths for its sides because two of the sides added together are not greater than the third side. Option C: Using the Triangle Inequality Theorem, we need to see if the sum of each of the combinations of two sides is greater than the other side: $1 + 2 > 4$ --> This statement is false. $2 + 4 > 1$ --> This statement is true. $1 + 4 > 2$ --> This statement is true. A triangle cannot have these lengths for its sides because two of the sides added together are not greater than the third side. Option D: Using the Triangle Inequality Theorem, we need to see if the sum of each of the combinations of two sides is greater than the other side: $3 + 5 > 7$ --> This statement is true. $5 + 7 > 3$ --> This statement is true. $3 + 7 > 5$ --> This statement is true. These lengths can form a triangle because the sum of two sides is always greater than the third side.