In the attached picture you find the two triangles. To check if the lengths of the sides are the same, we use the formula for the distance between two points:
[tex] d(A,B) = \sqrt{(A_x-B_x)^2+(A_y-B_y)^2} [/tex]
If we plug the values for the points of PQR, we have
[tex] \overline{PQ} \approx 5.39 [/tex]
[tex] \overline{QR} \approx 3.61 [/tex]
[tex] \overline{PR} \approx 7.07 [/tex]
Similarly, for STU we have
[tex] \overline{ST} \approx 5.1 [/tex]
[tex] \overline{TU} \approx 2.24 [/tex]
[tex] \overline{SU} \approx 6.71 [/tex]
As you can see, the lengths of the sides do not match, as a triplet, so the two triangles are not congruent.
