Short Answer 
Parallel lines are defined as lines that never intersect and have the same slope. In square EFGH, segments EF and GH, as well as EH and FG, are parallel due to their consistent slope of -1, which is critical for mathematical proofs involving the shape.
Step 1: Understand Parallel Lines
In Mathematics and Euclidean Geometry, parallel lines are defined as two lines that maintain the same distance from each other forever, without ever intersecting. For two lines to be classified as parallel, they must meet specific conditions:
- Both lines have the same slope.
- They will never touch, regardless of how far they are extended.
Step 2: Recognize Slopes in Quadrilaterals
In quadrilateral EFGH, it is identified as a square, which indicates that every side has a slope of -1 due to its geometric properties. This consistent slope applies to any pair of sides that are parallel to each other. Thus, the following pairs are parallel:
- Segment EF is parallel to segment GH (EF || GH).
- Segment EH is parallel to segment FG (EH || FG).
Step 3: Application in Proofs
When completing a mathematical proof concerning quadrilaterals or other geometric shapes, recognizing parallel relationships is crucial. In this case, it enables the conclusion that certain segments are parallel due to their identical slopes. As noted in the proof of statement 4, acknowledging EH || FG is significant in validating the properties of square EFGH.