Question

∠pqs is a right angle and qr ≅ pq. which term describes qs? angle bisector median altitude perpendicular bisector

Explanation:

Step1: Recall definitions

• Angle bisector: A line that divides an angle into two equal parts.
• Median: A line segment joining a vertex to the mid - point of the opposite side.
• Altitude: A perpendicular line segment from a vertex to the line containing the opposite side.
• Perpendicular bisector: A line that is perpendicular to a segment and bisects it.

Step2: Analyze the given information

We know that \(\angle PQS\) is a right angle (\(\angle PQS = 90^{\circ}\)) and \(QR\cong PQ\).
Let's consider the triangles \(\triangle RQS\) and \(\triangle PQS\).
Since \(QR = PQ\) (given) and \(QS=QS\) (common side) and \(\angle RQS=\angle PQS = 90^{\circ}\) (because \(\angle PQS\) is a right angle and we assume \(QS\) is constructed in a way that forms right angles with \(RQ\) and \(PQ\) based on the congruence and right - angle condition).
By the Hypotenuse - Leg (HL) congruence criterion for right - triangles (\(\triangle RQS\cong\triangle PQS\)), \(RS = PS\). Also, \(QS\perp RP\) (because \(\angle RQS=\angle PQS = 90^{\circ}\)).

Answer:

perpendicular bisector