Question

re - write the following statement as a conditional (\if - then\) statement. the longest side of a right triangle is the hypotenuse. a. if the figure has a hypotenuse, then it is a right triangle. b. if the figure is a right triangle, then it has exactly one hypotenuse. c. if the segment is the longest side of a triangle, then it is the hypotenuse. d. if the segment is the longest side of a right triangle, then it is the hypotenuse.

Explanation:

Step1: Analyze each option

• Option A: The original statement is about a right - triangle's longest side. This option reverses the logic (starts with hypotenuse to conclude right - triangle), which is not the same as the given statement.
• Option B: The original statement focuses on the relationship between the longest side of a right - triangle and the hypotenuse. This option is about the number of hypotenuses in a right - triangle, which is not the key point of the original statement.
• Option C: The original statement is specifically about a right - triangle. This option is about any triangle, so it is too general.
• Option D: It correctly takes the condition “the segment is the longest side of a right - triangle” (from the original statement “the longest side of a right - triangle”) and the conclusion “it is the hypotenuse” (from the original statement “is the hypotenuse”).

Answer:

D. If the segment is the longest side of a right triangle, then it is the hypotenuse.