The correct answer is B

Explanation

Consider each statement separately. For example, consider statement Roman numeral 1, A B plus C D equals A D. From the figure, you can see that segment A D is made up of the segments A B, B C, and C D. This tells you that A B plus C D cannot equal A D, since B C cannot equal zero. Statement Roman numeral 1 is not true.

Consider statement Roman numeral 2, A B plus B C equals A D minus C D. Since B is between A and C, it follows that A B plus B C equals A C. Since C is between A and D, it follows that A C plus C D equals A D. Therefore, A D minus C D equals A C. Since both A B plus B C and A D minus C D equal A C, they are equal to each other. Statement Roman numeral 2 is true.

Consider statement Roman numeral 3, A C minus A B equals A D minus C D. The left side of the equation, A C minus A B, is equivalent to B C. The right side of the equation, A D minus C D, is equivalent to A C. Since A B cannot equal zero, B C is not equal to A C. Statement Roman numeral 3 is not true.

Statement Roman numeral 2 is the only one that is true.