Question

use the understanding of similar figures to determine the corresponding angles and scale factor the figure on the left is the original

Answer 1

Similar Triangles : Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

In the given triangles ABC and DEF

side AB = 18, BC = 18, CA = 16

Side DE = 9, EF = 9, FD = 8

as the ratio of the sides ABC to the triangle DEF are :

`\begin{gathered} (AB)/(DE)=(18)/(9)=2 \\ (BC)/(EF)=(18)/(9)=2 \\ (CA)/(FD)=(16)/(8)=2 \\ \text{Thus, we get each cooresponding sides ratio are equal to 2} \end{gathered}`

From the defination of similar triangles :

A set of triangle is said to be similar if the ratio of corresponding sides of triangle are equal

As ratio = 2 thus the triangles ABC is similar to triangle DEF

Scale Ratio : When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles.

As the ratio of corresponding sides is equal to 2 thus

From the defination of scale factor :

Scale factor is 2

As the scale factor of the similar triangle for all sides are equal Thus,

`\text{ Scale factor for }(AB)/(DE)=(BC)/(EF)=(CA)/(FD)=2`

So, corresponding sides of similar triangles and scale factor are :

Answer :