Question

quiz 5.1 form a

1. \\( \overline { q s } \\) is a perpendicular bisector.

if \\( q p = 14, q r = \\)

1. \\( \overline { q s } \\) is an angle bisector. \\( r s = \\)

Explanation:

Step1: Use the perpendicular bisector theorem

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. Since \( \overline{QS} \) is a perpendicular bisector of \( \overline{PR} \), then \( QP = QR \). Given \( QP = 14 \), so \( QR=14 \).

Step2: Use the angle bisector theorem (distance from a point to sides of an angle)

If a point is on the bisector of an angle, then it is equidistant from the sides of the angle. Since \( \overline{QS} \) is an angle bisector, and \( SP\perp QP \), \( SR\perp QR \), then \( RS = PS \). Given \( PS = 20 \), so \( RS=20 \).

Answer:

1. \(14\)
2. \(20\)