Question

State the postulate or theorem that justifies each answer. If e (is perpendicular to) b, then e (is perpendicular to) c.

a) The Pythagorean Theorem
b) The Transitive Property of Perpendicular Lines
c) The Perpendicular Bisector Theorem
d) The Transitive Property of Equality

Answer 1

The correct justification when a line is perpendicular to two others at their intersection is the Transitive Property of Perpendicular Lines, indicating that those two lines must be parallel.

Step-by-step explanation:

If e is perpendicular to b, and e is also stated to be perpendicular to c, the theorem that justifies this statement is b) The Transitive Property of Perpendicular Lines. This property tells us that if a line is perpendicular to two other lines at their intersection, those two lines must be parallel. This is not to be confused with the Pythagorean Theorem, which relates the lengths of the sides of a right triangle, stating that a² + b² = c².