standard_description: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
problem_activity: Task
In the two triangles below, angle $A$ is congruent to angle $D$, side $AC$ is congruent to side $DF$ and side $AB$ is congruent to side $DE$:
[IMG]
Sally reasons as follows: "If angle $A$ is congruent to angle $D$ then I can move point $A$ to point $D$ so that side $AB$ lies on top of side $DE$ and side $AC$ lies on top of side $DF$. Since $AB$ and $DE$ are congruent as are $AC$ and $DF$ the two triangles match up exactly and so they are congruent.''
Explain Sally's reasoning for why triangle $ABC$ is congruent to triangle $DEF$ using the language of reflections:
Construct a reflection which maps point $A$ to point $D$. Call $B'$ and $C'$ the images of $B$ and $C$ respectively under this reflection.
Construct a reflection which does not move $D$ but which sends $B'$ to $E$.  Call $C''$ the image of $C'$ under this reflection.
Construct a reflection which does not move $D$ or $E$ but which sends $C''$ to $F$.


aligns: no