Solution:
Given ΔTUV and ΔTLM;
Where the side are measure are as follow below
[tex]\begin{gathered} TU=24\text{ units} \\ TV=36\text{ units} \\ TL=6\text{ units} \\ TM=9\text{ units} \end{gathered}[/tex]
The ratio of the sides, applying the proportionality formula will be
[tex]\begin{gathered} \frac{TL}{TU}=\frac{6}{24}=\frac{1}{4} \\ \frac{TM}{TV}=\frac{9}{36}=\frac{1}{4} \\ \frac{TL}{TU}=\frac{TM}{TV}=\frac{1}{4} \end{gathered}[/tex]
From the deductions above,
The sides are similar.
And
[tex]m\angle UTV=m\angle LTM\text{ \lparen verticala angles\rparen}[/tex]
Since, an angle is included, then
Then, they are similar and ΔTUV is similar to ΔTLM.
Hence, the triangles are similar; SAS similarity; ΔTLM
The answer is option A
