Question

The two figures are similar.

Answer 1

Given:

Two similar figures.

Solution:

Part a:  

ΔABC and ΔA'B'C' are similar.

Similarity statement:

If two triangles are similar, then the corresponding sides are in proportion.

$\frac{A B}{A^{\prime} B^{\prime}} = \frac{6}{24} =\frac{1}{4}$

$\frac{BC}{B^{\prime} C^{\prime}} = \frac{12}{48} =\frac{1}{4}$

$\frac{CA}{C^{\prime} A^{\prime}} = \frac{15}{60} =\frac{1}{4}$

The sides are in the same ratio. Therefore the two triangles are similar.

Part b:

The sides of A'B'C' are greater than the original image ABC.

Therefore, the dilation A'B'C' is an enlargement.

Part c:

Scale factor:

$K =\frac{\text {Side length of image }}{\text {Side length of original }}$

$K =\frac{A^{\prime}B^{\prime}}{AB}$

$K =\frac{24}{6}$

K = 4

Scale factor = 4

K > 1

Therefore the image of the dilation is enlargement.