Question

a, b, c, and d are distinct lines in the same plane. For each combination of relationships, tell how a and d relate. Justify your answer. a∥b,b⊥c,c⊥d

Answer 1

Lines a and d are parallel to each other because line a is parallel to line b which is perpendicular to line c, and line c is also perpendicular to line d.

Step-by-step explanation:

Given the relationships between lines a, b, c, and d: a∕∕b, b⊥c, c⊥d, we can deduce the relationship between lines a and d. Since line a is parallel to line b, and line b is perpendicular to line c, it follows that line a is also perpendicular to line c because parallel lines share the same angle relationships with any line that intersects them. Now, considering that line c is perpendicular to line d, and we have previously established that line a is perpendicular to line c, we can infer that lines a and d are parallel to each other. This is due to the transitive property where if a line is perpendicular to two lines that are perpendicular to each other, those two lines must be parallel to each other.