Question

State if the triangles are similar. If so, how do you know they are similar and complete the similarity statement.A. similar; SAS similarity; ΔTLMB. similar; SSS similarity; ΔTLMC. not similarD. similar; SAS similarity; ΔTML

Answer 1

Given ΔTUV and ΔTLM;

Where the side are measure are as follow below

`\begin{gathered} TU=24\text{ units} \\ TV=36\text{ units} \\ TL=6\text{ units} \\ TM=9\text{ units} \end{gathered}`

The ratio of the sides, applying the proportionality formula will be

`\begin{gathered} (TL)/(TU)=(6)/(24)=(1)/(4) \\ (TM)/(TV)=(9)/(36)=(1)/(4) \\ (TL)/(TU)=(TM)/(TV)=(1)/(4) \end{gathered}`

From the deductions above,

The sides are similar.

And

`m\angle UTV=m\angle LTM\text{ \lparen verticala angles\rparen}`

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