Question

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

Explanation:

Step1: Recall SSS Congruence Criterion

For two triangles to be congruent by SSS (Side - Side - Side), the corresponding sides must be equal. In \(\triangle PQR\), \(PQ = 9\), \(PR=12\), and \(QR = 15\). So, for \(\triangle XYZ\) to be congruent to \(\triangle PQR\) by SSS, \(XY\) must correspond to \(PQ\), \(XZ\) must correspond to \(PR\), and \(YZ\) must correspond to \(QR\).

Step2: Match the Sides

Since \(PQ = 9\), \(PR = 12\), \(QR=15\), we need \(XY = 9\), \(XZ = 12\), \(YZ = 15\).

Answer:

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