A builder designs two triangular tiles, represented by \(\Delta XYZ\) and \(\Delta PQR\). The angles of the first tile \(\Delta XYZ\) are \(\angle X = 50^\circ\), \(\angle Y = 60^\circ\) and \(\angle Z = 70^\circ\). The second tile \(\Delta PQR\) also has angles \(\angle P = 50^\circ\), \(\angle Q = 60^\circ\) and \(\angle R = 70^\circ\).
The first tile has sides measuring \(XY = 30 \ cm\), \(YZ = 35 \ cm\) and \(XZ = 40 \ cm\), while the second tile has sides measuring \(PQ = 6 \ cm\), \(QR = 7 \ cm\) and \(PR = 8 \ cm\).
Are the two tiles congruent?
Reason: Since each side of the first triangle is the corresponding side of the second triangle.