1. **Problem Statement:** Classify the segments \(\overline{KM}\), \(\overline{CD}\), and \(\overline{PS}\) in their respective triangles based on the given figure and markings. 2. **Key Definitions:** - A **perpendicular bisector** is a segment that is perpendicular to a side and bisects it (divides it into two equal parts). - An **angle bisector** divides an angle into two equal angles. - A **median** connects a vertex to the midpoint of the opposite side. - An **altitude** is a perpendicular segment from a vertex to the line containing the opposite side. 3. **Analyze \(\overline{KM}\) in \(\triangle JKL\):** - \(\overline{KM}\) is drawn from vertex K to side JL. - There is a right angle at M, so \(\overline{KM}\) is perpendicular to JL. - Since M is on JL and the segment is perpendicular, \(\overline{KM}\) is an altitude. - No indication that M is the midpoint, so it is not necessarily a median or perpendicular bisector. - No indication that \(\overline{KM}\) bisects \(\angle K\). 4. **Analyze \(\overline{CD}\) in \(\triangle ABC\):** - \(\overline{CD}\) is drawn from vertex C to side AB. - There is a right angle at D, so \(\overline{CD}\) is perpendicular to AB. - Since D lies on AB and the segment is perpendicular, \(\overline{CD}\) is an altitude. - No indication that D is the midpoint, so it is not necessarily a median or perpendicular bisector. - No indication that \(\overline{CD}\) bisects \(\angle C\). 5. **Analyze \(\overline{PS}\) in \(\triangle PQR\):** - \(\overline{PS}\) is drawn from vertex P to side QR. - There is a right angle at S, so \(\overline{PS}\) is perpendicular to QR. - Since S lies on QR and the segment is perpendicular, \(\overline{PS}\) is an altitude. - No indication that S is the midpoint, so it is not necessarily a median or perpendicular bisector. - No indication that \(\overline{PS}\) bisects \(\angle P\). **Final classifications:** - \(\overline{KM}\): Altitude of \(\triangle JKL\) - \(\overline{CD}\): Altitude of \(\triangle ABC\) - \(\overline{PS}\): Altitude of \(\triangle PQR\)