Question

10 points really easy question just asking if they are congurent please help Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(4, 0), Q(0, −4), and R(−8, −4). Triangle P'Q'R' has vertices P'(1, 0), Q'(0, −1), and R'(−2, −1). Plot triangles PQR and P'Q'R' on your own coordinate grid. Part C: Are the two triangles PQR and P''Q''R'' congruent? Explain your answer. (2 points)

Answer 1

They are not congruent; they are similar.

Explanation:

If you analyze the coordinates, you can see that Triangle PQR has been dilated by 1/4 to become Triangle P'Q'R'. Because the triangle has been dilated but not transformed in any other way, you can say that the triangles are similar, but not congruent.

To be congruent, the triangles would have to have the same sizes and the same lengths (you may refer to the diagram below for a visual reference). To be similar, the triangles would have to have the same angles, but with different side lengths. With the dilation, the side lengths have changed, but the angles have not changed.

Hope this helps!