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Savatey [412]
3 years ago
10

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

Mathematics
2 answers:
kogti [31]3 years ago
5 0
<span>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.</span>
AveGali [126]3 years ago
3 0

Answer: If an image of a triangle is congruent to the pre-image, then the scale factor of the dilation must be n =  <u>1</u>.

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 , \frac{\text{pre-image}}{\text{image}}=n, \text{where n is the scale factor.}...........(1)

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

Then \frac{\text{pre-image}}{\text{image}}=\frac{AB}{A'B'}=\frac{BC}{B'C'}=\frac{AC}{A'C'}=1.......(2)

From (1) and (2),  n=1

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

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