Question 23 of 25 Line s is the perpendicular bisector of JK. If line s intersects JK at point L, which of the following statements must be true? Check all that apply. A. Line s is perpendicular to JK B. Line s intersects JK at a 180° angle C. Line s is parallel to JK D. Point L is the midpoint of JK E. JL = KL

Question 23 of 25 Line s is the perpendicular bisector of JK. If line s intersects JK at point L, which of the following statements must be true? Check all that apply. A. Line s is perpendicular to JK B. Line s intersects JK at a 180° angle C. Line s is parallel to JK D. Point L is the midpoint of JK E. JL = KL

Answer: A, D, E

Explanation: Subject: Geometry. Relevant concept: perpendicular bisector (and the Perpendicular Bisector Theorem). By definition, a perpendicular bisector of segment JK is a line that (1) is perpendicular to JK and (2) bisects JK (cuts JK into two equal parts). Therefore:

  • A is true because “perpendicular bisector” means the line is perpendicular to JK.
  • D is true because “bisector” means it meets JK at its midpoint.
  • E is true because if L is the midpoint then \(JL = KL\).

B is false because intersection at a 180° angle would be a straight (collinear) angle, not perpendicular (which is 90°). C is false because a perpendicular bisector cannot be parallel to the segment it bisects.

Steps:

  1. State definition: A perpendicular bisector of segment JK is a line that is perpendicular to JK and passes through JK’s midpoint.
  2. From the definition, line s is perpendicular to JK → select A.
  3. From the definition, line s intersects JK at its midpoint L → select D.
  4. Midpoint L implies the two segments are equal: \(JL = KL\) → select E (Perpendicular Bisector Theorem also implies any point on the perpendicular bisector is equidistant from J and K).
  5. Reject B: intersection at 180° is incorrect (perpendicular means 90°).
  6. Reject C: a line parallel to JK cannot be perpendicular and cannot bisect JK where they don’t meet.
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