Question

mark the figure to show the given information. explain how you would prove ( angle p cong angle q ).
given: ( overline{kl} ) is the perpendicular bisector of ( overline{pq} )
which figure below has the correct marks to show the given information?
oa.
ob.
oc.
od.

Explanation:

Step1: Analyze the given information

Given that \( \overline{KL} \) is the perpendicular bisector of \( \overline{PQ} \). A perpendicular bisector means two things: \( KL\perp PQ \) (so there is a right - angle at \( L \)) and \( PL = LQ \) (so \( \overline{PL}\) and \( \overline{LQ}\) should have the same marking).

Step2: Check each option

• Option A:
• It shows \( KL\perp PQ \) (right - angle at \( L \)) and \( PL = LQ \) (equal markings on \( PL\) and \( LQ\)).
• Option B:
• The markings on \( PK\) and \( QK\) are incorrect. The given is about the perpendicular bisector of \( PQ\), not about \( PK\) and \( QK\).
• Option C:
• The angle markings are incorrect. The given is about a perpendicular bisector (a segment - related property, not an angle - related property initially for marking the given information).
• Option D:
• The markings on \( PK\) and \( QK\) are wrong. The key information is \( KL\) is the perpendicular bisector of \( PQ\) (right - angle at \( L\) and \( PL = LQ\)), not about \( PK\) and \( QK\).

Answer:

A.