Question

The vertices of ΔGHI are G (2, 4), H (4, 8), and I (8, 4). The vertices of ΔJKL are J (1, 1), K (2, 3), and L (4, 1). Which conclusion is true about the triangles?
They are congruent by the definition of congruence in terms of rigid motions.
They are similar by the definition of similarity in terms of a dilation.
The ratio of their corresponding sides is 1:3
The ratio of their corresponding angles is 1:3.

Answer 1

Answer:

They are similar by the definition of similarity in terms of a dilation.

Step-by-step explanation:

The first step is finding the sides of each triangle.

In triangle GHI, we have that:

GH = sqrt((4-2)^2 + (8-4)^2) = 4.4721

HI = sqrt((8-4)^2 + (4-8)^2) = 5.6569

IG = sqrt((2-8)^2 + (4-4)^2) = 6

Now, for the triangle JKL, we have:

JK = sqrt((2-1)^2 + (3-1)^2) = 2.2361

KL = sqrt((4-2)^2 + (1-3)^2) = 2.8284

LJ = sqrt((1-4)^2 + (1-1)^2) = 3

The triangles are not congruent, because the sides are different

They are similar, because their sides have a proportion (sides of GHI are 2 times the sides of JKL). If they are similar, they have the same angles.

The ratio of their corresponding sides is 1:2, not 1:3

The ratio of their corresponding angles is 1:1, not 1:3