If an image of a triangle is congruent to the pre-image, then the scale factor of the dilation must be n =
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If an image of a triangle is congruent to the pre-image, then the scale factor of the dilation must be n = 1. Dilating an image with a dilation factor of 1 will result to the same image and that ensures the congruency between the pre-image and the dilated image.

If an image of a triangle is congruent to the pre-image, then the scale factor of the dilation must be n =  1.

Step-by-step explanation:

A dilation is a transformation that creates an image that is the same shape as the original, but is a different size.

Since in a dilation, the corresponding the sides of the pre-image and  sides of the image are proportional.

Such that , ...........(1)

Let ΔABC is dilated to ΔA'B'C' such that AB≅A'B', BC≅B'C' and AC≅B'C'.

Then .......(2)

From (1) and (2),  

Therefore, If an image of a triangle is congruent to the pre-image, then the scale factor of the dilation must be n =  1.

The answer of the above is

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