standard_description: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
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