If the two triangles are similar by hypotenuse-leg similarity, what is the value of X?

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

These two triangles are similar by AA similarity. The ratio of corresponding altitudes is proportion to the ratio of corresponding sides. Find the value of x.

AB=15, PQ=7.5
AC=17, PR=x

Are the triangles similar? If yes, write a similarity statement and explain how you know they are similar.

Determine which method (${\displaystyle \mathrm{\forall }\stackrel{\sim }{=}\mathrm{\forall }}$, SAS Theorem of Similarity, SSS Theorem of Similarity) proves that the following triangles are similar.

To check: whether the triangles are similar. If so, write a similarity statement.
Given:
The given triangles are:

To Complete:the statement WZ=? and RS=? in the figure shown.
Given:
Figure is shown below.

RW=15, ZR=10 and ZS=8

Find c.
Given: