Select the true statement. Dilations of an angle must be congruent to the original angle. Dilations of a triangle must be congruent to the original triangle Dilations of a segment must be congruent to the original segment. Dilations of a circle must be congruent to the original circle.

The true statements is;

Dilations of an angle must be congruent to the original angle

Step-by-step explanation:

Given that an angle is formed by the intersection of two rays, and that the ratio of the sides of a figure, before and after a dilation are the same, for an angle in a triangle we have, by sine rule;

a/(sin(α)) = b/(sin(β)) = c/(sin(γ))

Rearranging, gives;

a/b = (sin(α))/(sin(β))

Whereby for the dilation, we have;

a'/b' = (sin(α'))/(sin(β'))

We  have;

a/b = a'/b'

∴ (sin(α))/(sin(β)) = (sin(α'))/(sin(β'))

Similarly, we have;

(sin(β))/(sin(γ)) = (sin(β'))/(sin(γ'))

(sin(α))/(sin(γ)) = (sin(α'))/(sin(γ'))

Given that α, β, and γ, are less than 180°, we have

α = α'

∴ α ≅ α' by definition of congruency

β = β'

β ≅ β' by definition of congruency

γ = γ'

γ ≅ γ' by definition of congruency

Therefore; dilations of an angle must be congruent to original angle

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step-by-step explanation:

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