two segments that are not congruent, their sum and their difference. Then subtract from the sum of the difference between them and verify that the segment obtained is twice the lower segment.
To solve this problem, let's start by assuming that we have two line segments, segment A and segment B, which are not congruent.
1. Let's denote the length of segment A as "a" and the length of segment B as "b".
2. The sum of segment A and segment B is given by: a + b.
3. The difference between segment A and segment B is given by: a - b.
Now, we want to subtract the sum of the difference of segments A and B from the difference itself and verify that the resulting segment is twice the length of the smaller segment.
Let's calculate step by step:
1. Subtract the sum of the difference of segments A and B from the difference:
(a - b) - (a + b)
Simplifying this expression, we get:
a - b - a - b
2. Now, simplify further by combining like terms:
-2b - 2b
3. The resulting expression is:
-4b
To verify if this resulting segment is twice the length of the smaller segment, we need to compare it with the smaller segment.
4. Comparing the resulting segment (-4b) with the smaller segment:
-4b = 2 * (smaller segment)
If the resulting segment is indeed twice the length of the smaller segment, this equation should hold true.
Thus, we can conclude that the resulting expression, -4b, is twice the length of the smaller segment.
Note: This conclusion is based on the assumption that the given segments A and B are non-congruent and that the calculations were done correctly.