Question

The vertices of δABC are a(1,–2), b(1,1), and c(5,–2). Which could be the side lengths of a triangle that is similar but not congruent to δABC?

(a) 4, 3, 4
(b) 2, 1, 2
(c) 5, 1, 5
(d) 6, 2, 6

Answer 1

In order for a triangle to be similar but not congruent to a given triangle, the corresponding sides must be proportional but not equal in length. Out of the given choices, the side lengths of triangle ABC can be similar but not congruent to the side lengths of triangle ABC.

Step-by-step explanation:

In order for a triangle to be similar but not congruent to ΔABC, the corresponding sides must be proportional but not equal in length.

Let's calculate the side lengths of ΔABC:

Side AB = sqrt((1 - 1)^2 + (1 - (-2))^2) = sqrt(0 + 9) = 3

Side BC = sqrt((5 - 1)^2 + ((-2) - 1)^2) = sqrt(16 + 9) = sqrt(25) = 5

Side AC = sqrt((5 - 1)^2 + ((-2) - (-2))^2) = sqrt(16 + 0) = 4

Out of the given choices, only option (a) 4, 3, 4 satisfies the condition of being proportional but not equal in length to the sides of ΔABC.