Question

Given the coordinates, determine whether PQR & XYZ are congruentP(5,-4), Q(-3, 7), R(0, 2), X(-2,-1), Y(9, 7), Z(3, 2)PQ=XY=QR=YZ=PR=XZ= Are the triangles congruent? If yes, explain your reasoning and write a congruence statement.

Answer 1

Answer: Let's see. The triangle QRZ (I will call it triangle qrz from now on) must be congruent to the triangle YXZ (that I will call triangle yxz from now). Why is this? Because if you compare side qr to yx, you will see that qr side is longer than yx side. Now do the same kind of comparison with every corresponding side. For example, zy side is longer than pz side. So we can say the triangle qrz is congruent to the triangle yxz.

Answer 2

At first, we will use the rule of distance to find the sides of the 2 triangles

`d=\sqrt[]{(x2-x1)^2+(y2-y1)^2}`

If PQ = XY,

QR = YZ

PR = XZ

Then the 2 triangles are congruent using SSS postulate of congruency

If any two sides not equal, then

Triangles are not congruent