Reiny ..thanks for the formula and example. I tried it and i get that both sets of triangles are congruent but

Question

it is multiple choice with one answer. I don't know what i am doing wrong.
How do I determine which two triangles on a graph are congruent. ∆QRS and ∆DEF or ∆ABC and ∆XYZ.
i found the coordinates of both sets:
QRS Q(-2,5), R(-2,1), S(-5, 1)
DEF D(5,-6), E(5,-2), F(2,-2)
or
ABC A(4,5), B(6,2), C(2,2)
XYZ X(-4,-5), Y(-6,-2), Z(-2,-2)

Answer 1

Let's see what's what here...

QR = √((-2+2)^2 + (1-5)^2) = √16
RS = √((-5+2)^2 + (1-1)^2) = √9
SQ = √((-2+5)^2 + (5-1)^2) = √25

DE = √((5-5)^2 + (-2+6)^2) = √16
EF = √((2-5)^2 + (-2+2)^2) = √9
FD = √((5-2)^2 + (-6+2)^2) = √25

So, QRS ≅ DEF

AB = √((6-4)^2 + (2-5)^2) = √13
BC = √((2-6)^2 + (2-2)^2) = √16
CA = √((4-2)^2 + (5-2)^2) = √13

XY = √((-6+4)^2 + (2+5)^2) = √13
YZ = √((-2+6)^2 + (-2+2)^2) = √16
ZX = √((-4+2)^2 + (-5+2)^2) = √13

So, ABC ≅ XYZ

So, assuming there are no typos, you are correct and the answer key is wrong.

In this case QRS and DEF are easy, since they are right triangles with legs parallel to the axes, and are easy to measure.

ABC and XYZ are just reflected through the origin (the coordinates have just changed signs), so they also must be congruent.

Answer 2

Ok..great..thx for checking.