Question

Determine whether the following statement is always, sometimes, or never true
If B is between A & C, then AC+AB = BC.

Answer 1

If B is in between A and C, then AC + AB = BC can't be true because AC is the whole and it is being added to AB which is a part. BC is also a part so it would not make sense if the whole thing plus a part of it is equal to a part. Ex. Say AC is 8, AB is 3, and BC is 5. Putting this numbers in their place would make it 8 + 3 = 5 which is definitely not true.

2. Sometimes true
In a linear pair, the angles have to be adjacent( next to each other). However, in a parallelogram and in a quadrilateral that is inscribed in a circle, that isn't true. It is the opposite angles that are supplementary but they are not adjacent. But two angles that are supplementary can form a linear pair so it is only sometimes true.

3. Always true
The two angles formed by the intersecting lines are congruent and they are adjacent. Knowing that, I can conclude that they are right angles because for them to be congruent they each have to be 90 degrees (180/2 = 90). Perpendicular lines intersect to form right angles so it is always true. There are no exceptions.

*Sorry, I write a lot.