We can find the lengths of the other sides in a similar way. Before we find the lengths, notice that the exercise asks about the congruence in a specific order.
△ STU ? ≅△ XYZ
This means that we need to check the lengths between the corresponding sides to see if each segment is congruent.
Corresponding Side
Distance Formula
Result
ST and XY
sqrt((0-0)^2+(0-5)^2) ? = sqrt((4-4)^2+(3-8)^2)
5= 5
TU and YZ
sqrt((1-0)^2+(1-0)^2) ? = sqrt((6-4)^2+(3-3)^2)
sqrt(2)≠ 2
US and ZX
sqrt((0-1)^2+(5-1)^2) ? = sqrt((4-6)^2+(8-3)^2)
sqrt(17)≠ sqrt(29)
Since not all of the side lengths of △ STU match all of the side lengths of △ XYZ, the triangles are not congruent.
△ STU ≆△ XYZ
