Explain how to construct a triangle that is congruent to \triangle OBT

Solve the formula for the indicated variable.
Formula for the volume of a cylinder, ${\displaystyle V=\pi r^{2}h}$, for h

The circumference of two circles are ${\displaystyle 12\pi }$ and ${\displaystyle 36\pi }$. Find the ratio of the areas of the circles.
a) ${\displaystyle 1:3}$
b) ${\displaystyle 1:9}$
c) ${\displaystyle 3:4}$
d) ${\displaystyle 2:5}$

Decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Theorem.

State if the triangles are similar. If so state how you know they are similar and complete the similarity statement.

Non-geometric way to calculate expected value of breaks?
"A bar is broken at random in two places. Find the average size of the smallest, of the middle-sized, and of the largest pieces."
The author gives what seems like a complicated geometric way of calculating the probabilities. He arrives at the solutions 1/9, 5/18, and 11/18. Is there a simpler, non-geometric way of calculating these probabilities?

To construct:
The angle equal to the average of measures of ${\displaystyle \mathrm{\angle }A}$ and ${\displaystyle \mathrm{\angle }B}$.

Determine whether the congruence is true or false. $5\equiv 8mod3$