Question

name date period 11. writing in math if line a is parallel to line b and ∠1 ≅ ∠2, describe the relationship between lines b and c. explain your reasoning.

Explanation:

Step1: Analyze ∠1 and ∠2

∠1 and ∠2 are adjacent angles forming a linear pair? Wait, no, ∠1 ≅ ∠2 and they are vertical? Wait, no, looking at the diagram, ∠1 and ∠2 are adjacent and form a linear pair? Wait, no, if ∠1 ≅ ∠2, and they are supplementary (since they form a linear pair, sum to 180°), so if ∠1 = ∠2, then each is 90°. So line a is perpendicular to line c (since ∠1 and ∠2 are 90°, so a ⊥ c).

Step2: Use a || b

Since line a is parallel to line b, and a is perpendicular to c, then by the property of parallel lines, if a line is perpendicular to one of two parallel lines, it is perpendicular to the other. So b is also perpendicular to c.

Answer:

Lines \( b \) and \( c \) are perpendicular. Reasoning: Since \( \angle 1 \cong \angle 2 \) and \( \angle 1 + \angle 2 = 180^\circ \) (linear pair), \( \angle 1 = \angle 2 = 90^\circ \), so \( a \perp c \). As \( a \parallel b \), a line perpendicular to \( a \) (line \( c \)) is also perpendicular to \( b \), so \( b \perp c \).