Are the two triangles similar? If so, by what similarity shortcut?

Find the point on the line $y=2x+3$ that is closest to the origin.

Find the length x. 

To calculate:The ratio of line AB and AC.
Given information:

To find: The values of KP, KM, MR, ML, MN and PR.
Given:

${\displaystyle \overline{PR}\mid \mid \overline{KL}=9,\ln =16,PM=2\left(KP\right)}$
KM=KP+PM=3KP

Are the two triangles similar? If yes, then complete the similarity statement.
Select all that apply.
${\displaystyle \mathrm{△}RQP\sim \mathrm{△}}$? by ? similarity

The triangles are not similar.
${\displaystyle \mathrm{△}FED}$
${\displaystyle \mathrm{△}EFD}$
by SAS similarity
by SSS similarity
by AA similarity

To prove:The extended proportions that are needed to prove ${\displaystyle \mathrm{△}RST\sim \mathrm{△}XYZ}$ by the SSS similarity theorem.
Given ${\displaystyle \mathrm{△}RST,\mathrm{△}XYZ}$ are two triangles.

To determine:The difference and similarity between the graphs of the equations ${\displaystyle \frac{x^2}{9}-\frac{y^2}{1}=1\text{and}\frac{{(x-3)}^2}{9}-\frac{{(y+3)}^2}{1}=1}$