Question

1. triangle pqr has sides pq = 9, pr = 12, and qr = 15. for triangle xyz to be congruent to triangle pqr by sss, which of the following must be true?

a. xy = 12, xz = 15, yz = 9
b. xy = 9, xz = 12, yz = 15
c. xy = 9, xz = 15, yz = 12
d. xy = 15, xz = 9, yz = 12

Explanation:

Step1: Recall SSS Congruence Rule

SSS (Side - Side - Side) congruence rule states that if the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent. For \(\triangle PQR\) with \(PQ = 9\), \(PR=12\), and \(QR = 15\), we need to match the sides of \(\triangle XYZ\) such that \(XY = PQ\), \(XZ=PR\), and \(YZ = QR\).

Step2: Match the Sides

If \(\triangle XYZ\cong\triangle PQR\) by SSS, then \(XY = PQ = 9\), \(XZ=PR = 12\), and \(YZ=QR = 15\).

Answer:

b. \(XY = 9\), \(XZ = 12\), \(YZ = 15\)