Are pairs of triangles similar?Given information:12210202781.jpg

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

Find the volume of the described solid. A cap of a sphere with radius and height h

Write an informal proof to show triangles ABC and DEF are similar.

Given,
${\displaystyle \mathrm{△}ABC}$ with AB=4, BC=6 and CA = 2
${\displaystyle \mathrm{△}DEF}$ with DE=2, EF=3 and FD = 1
We have to prove the two triangles are similar.

Proving Similarity in the figure DEFG is a square. Prove the following:
${\displaystyle \mathrm{△}ADG\sim \mathrm{△}FEB}$
Given:
The given figure is,

Given ${\displaystyle \mathrm{△}ABC\sim \mathrm{△}QRS}$ what is the value of x?

Are pairs of triangles similar?
Given information:

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

SSS
SAS
AA
Not Similar