Question

1. figure lmn is dilated by a scale factor of 1/2. figure lmn is larger / smaller than figure lmn, because the scale factor is: between 0 and 1 / greater than 1. (circle one)
2. figure fgh is dilated by a scale factor of 1/4. figure fgh is larger / smaller than figure lmn, because the scale factor is: between 0 and 1 / greater than 1. (circle one)
3. square abcd is dilated by a scale factor of 1/2 with the origin as the center of dilation to create square abcd.

• square abcd is (congruent / similar) to square abcd.
• each side length of square abcd is (congruent to / 1/2 the) corresponding side length of square abcd. (circle one)
• each angle measure of square abcd is (congruent to / 1/2 the) corresponding angle measure of square abcd. (circle one)

Explanation:

Step1: Recall dilation rules

If the scale - factor \(k\) of a dilation satisfies \(01\), the dilated figure is larger. Also, for a dilation with scale - factor \(k\), the dilated figure and the original figure are similar. The side - lengths of the dilated figure are \(k\) times the side - lengths of the original figure, and the angle measures are congruent.

Step2: Analyze problem 3

The scale factor of the dilation of figure \(LMN\) is \(\frac{3}{2}=1.5>1\). So, figure \(L'M'N'\) is larger than figure \(LMN\) because the scale factor is greater than 1.

Step3: Analyze problem 4

The scale factor of the dilation of figure \(FGH\) is \(\frac{1}{4}\), and since \(0<\frac{1}{4}<1\), figure \(F'G'H'\) is smaller than figure \(FGH\) because the scale factor is between 0 and 1.

Step4: Analyze problem 5

When square \(ABCD\) is dilated by a scale factor of \(\frac{1}{2}\) with the origin as the center of dilation to create square \(A'B'C'D'\):

• Square \(A'B'C'D'\) is similar to square \(ABCD\) because dilation creates similar figures.
• Each side - length of square \(A'B'C'D'\) is \(\frac{1}{2}\) the corresponding side - length of square \(ABCD\) since the scale factor is \(\frac{1}{2}\).
• Each angle measure of square \(A'B'C'D'\) is congruent to the corresponding angle measure of square \(ABCD\) because angle measures are preserved under dilation.

Answer:

1. Larger; greater than 1
2. Smaller; between 0 and 1
3. Similar; \(\frac{1}{2}\) the; congruent to