Question

if an image of a triangle is congruent to the pre - image, what is the scale factor of the dilation?
0.1
$\frac{1}{2}$
1
10

Explanation:

Step1: Define congruent figures

Congruent figures have identical side lengths and angles, so their corresponding linear measurements are equal.

Step2: Relate to dilation scale factor

For a dilation, the side length of the image is $\text{scale factor} \times \text{pre-image side length}$. Let the pre-image side be $s$, image side be $s'$. Since $s' = s$, substitute into the dilation formula:
$$s = k \times s$$

Step3: Solve for scale factor $k$

Divide both sides by $s$ (where $s
eq 0$):
$$k = \frac{s}{s} = 1$$

Answer:

1