Answer:
See answers below
Step-by-step explanation:
By definition, two triangles are similar if all their corresponding angles are congruent and their corresponding sides are proportional. It is not necessary to check all angles and sides in order to tell if two triangles are similar. In fact, if you know only that all sides are proportional, that is enough information to know that the triangles are similar. This is called the SSS Similarity Theorem.
SSS Similarity Theorem
If all three pairs of corresponding sides of two triangles are proportional, then the two triangles are similar.
Looking at the two triangles we see that two of the sides of ΔDTC are in proportion to the corresponding two sides of ΔRLF
[tex]\dfrac{RF}{TC} = \dfrac{6}{8} = \dfrac{3}{4}[/tex]
[tex]\dfrac{RL}{DC} = \dfrac{12}{16} = \dfrac{3}{4}[/tex]
if we are given DT and FL and DT/FL = 3/4 then by SSS all three pairs of corresponding sides are equal and hence the two triangles are similar
We will be using the SSS similarity theorem to prove this
