Question

decide if there is enough information to conclude that p lies on the perpendicular bisector of qr. which of these statements is correct? no, you need to know at least one more angle measure of each triangle in order to conclude that p lies on the perpendicular bisector of qr. no, you need to know the length of one of the other sides of the triangles in order to conclude that p lies on the perpendicular bisector of qr. yes, these are both right triangles which means that p is perpendicular to qr. yes, the distances from the endpoints are the same for both sides of the triangle. every point on the segment is equal distance from the endpoints.

Explanation:

Step1: Recall perpendicular - bisector theorem

The perpendicular - bisector theorem states that a point is on the perpendicular bisector of a segment if and only if it is equidistant from the endpoints of the segment.

Step2: Analyze the statements

To conclude that point \(P\) lies on the perpendicular bisector of \(QR\), we need to know that the distances from \(P\) to \(Q\) and \(P\) to \(R\) are equal. Just having right - triangles or knowing angle measures is not sufficient.

Answer:

No, you need to know the distance from the endpoints are the same for both sides of the triangle. Every point on the segment is equal distance from the endpoints.