Question

Triangle ABC can be taken to triangle A’B’C using rigid motions and a dilation. Select the THREE equations that are true.

a) AB = A'B'
b) ∠ABC = ∠A'B'C'
c) AC + BC = A'C' + B'C'
d) AB = A'C'
e) ∠ABC = ∠B'C'
f) AC = A'B'

Answer 1

In triangle ABC, the equations AB = A'B' and ∠ABC = ∠A'B'C' are true when taking it to triangle A'B'C' using rigid motions and a dilation.

Step-by-step explanation:

In triangle ABC, we can take it to triangle A'B'C' using rigid motions and a dilation. Let's analyze the given equations to determine which ones are true:

1. AB = A'B': This equation is true because the corresponding sides of congruent triangles are equal.
2. ∠ABC = ∠A'B'C': This equation is true because the corresponding angles of congruent triangles are equal.
3. AB = A'C': This equation is false because there is no given information that suggests the side AB is equal to the side A'C'.

Therefore, the correct options are a) AB = A'B' and b) ∠ABC = ∠A'B'C'.