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

A wire is attached to the top of a pole. The wire is 7 ft longer than the pole, and the distance from the wire to the bottom of the pole is 7 ft less than the height of the pole. Find the length of the wire and the height of the pole.

The length of the wire is ? ft, and the height of the pole is ? ft.

If A, B, and C are the vertices of a triangle, find $\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CA}$

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

SSS
SAS
AA
Not Similar

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

The triangles are similar. The similarity ratio from A to B is ${\displaystyle \frac{4}{5}}$. Solve for x.