Which statements are true about dilations? Select all that apply.
Which statements are true about dilations? Select all that apply.
The correct option is E Dilations produce images that have sides that are proportional to the pre-image
Explanation for correct option:
Dilation is the process of creating same image of different size .
According to the definition of dilation :
Dilations creates images that have sides that are proportional to the pre-image because of the length of the sides of similar figure are always in a same proportion.
Dilation creates images that have angles that are congruent to the pre-image because of the similar figures have same corresponding angles but the sides are different.
Dilation creates images that are similar to the pre-image.
Option A: Dilations produce images that are similar to the pre-image.
From the definition of dilation it is clear that Dilation creates images that are similar to the pre-image.
So option A is correct.
Option C: Dilations produce images that have angles that are congruent to the pre-image.
From the definition of dilation it is clear that Dilation creates images that have angles that are congruent to the pre-image because of the similar figures have same corresponding angles but the sides are different.
So option C is correct.
Option E: Dilations produce images that have sides that are proportional to the pre-image
From the definition of dilation it is clear that Dilations creates images that have sides that are proportional to the pre-image because of the length of the sides of similar figure are always in a same proportion.
So option E is correct.
Explanation for incorrect option:
Option B: Dilations produce images that are always congruent to the pre-image.
Dilations does not creates images that are always congruent to the pre-image.
So option B is incorrect
Option D: Dilations produce images that have sides that are congruent to the pre-image.
Dilations does not creates images that have sides that are congruent to the pre-image.
So option D is incorrect
Hence option A , C and E are correct.
Dilations produce images that have sides that are proportional to the pre-image
Explanation for correct option:
Dilation is the process of creating same image of different size .
According to the definition of dilation :
Dilations creates images that have sides that are proportional to the pre-image because of the length of the sides of similar figure are always in a same proportion.
Dilation creates images that have angles that are congruent to the pre-image because of the similar figures have same corresponding angles but the sides are different.
Dilation creates images that are similar to the pre-image.
Option A: Dilations produce images that are similar to the pre-image.
From the definition of dilation it is clear that Dilation creates images that are similar to the pre-image.
So option A is correct.
Option C: Dilations produce images that have angles that are congruent to the pre-image.
From the definition of dilation it is clear that Dilation creates images that have angles that are congruent to the pre-image because of the similar figures have same corresponding angles but the sides are different.
So option C is correct.
Option E: Dilations produce images that have sides that are proportional to the pre-image
From the definition of dilation it is clear that Dilations creates images that have sides that are proportional to the pre-image because of the length of the sides of similar figure are always in a same proportion.
So option E is correct.
Explanation for incorrect option:
Option B: Dilations produce images that are always congruent to the pre-image.
Dilations does not creates images that are always congruent to the pre-image.
So option B is incorrect
Option D: Dilations produce images that have sides that are congruent to the pre-image.
Dilations does not creates images that have sides that are congruent to the pre-image.
So option D is incorrect
Hence option A , C and E are correct.
