Triangle Action

We learned that if one figure is [b]congruent[/b] to another it can be transformed to the other using [b]a sequence of rigid transformations[/b]. In other words, if two figures are congruent we can map one onto the other using only [b]translations[/b], [b]reflections[/b] and [b]rotations[/b]. Let's use this to answer the questions below:

Which [b]rigid transformation [/b]takes △[math]DEF[/math] to △[math]MNO[/math]? (Please select 2 choices)

Translation along [math]\vec{DM}[/math] Translation along [math]\vec{FO}[/math] [math]90^\circ[/math] Rotation about the origin Translation along [math]\vec{DN}[/math] Reflection across [math]\overline{ON}[/math]

Which rigid transformation shows that △[math]PQR[/math] is congruent to △[math]E_1D_1F_1[/math]? (Please select 2 choices)

Reflection across [math]\overline{WZ}[/math] [math]180^\circ[/math] rotation clockwise about point [math]V[/math] [math]90^\circ[/math] rotation clockwise about about point [math]Q[/math] [math]180^\circ[/math] rotation counter clockwise about point [math]V[/math] Translation along [math]\vec{PE_1}[/math]

Which shape is not congruent to any of the others?

△[math]E_1D_1F_1[/math] △[math]A_1B_1C_1[/math] △[math]EDF[/math] △[math]ABC[/math]

Which sequence of transformations does [u][b]not[/b][/u] show that △[math]JKL[/math] is congruent to △[math]STU[/math]? (The triangles have been provided again below for convenience)

Translation of △[math]JKL[/math] along [math]\vec{JS}[/math] followed by a reflection across [math]\overline{SU}[/math] Reflection of △[math]STU[/math] across [math]\overline{PQ}[/math] followed by a reflection across [math]\overline{RQ}[/math] Reflection of △[math]JKL[/math] across [math]\overline{JL}[/math] followed by a translation along [math]\vec{LU}[/math] Translation of △[math]STU[/math] along [math]\vec{TK}[/math] followed by a [math]90^\circ[/math]rotation clockwise about [math]K[/math]

[left][/left]Consider the triangles below. They have been constructed in such a way that guarantees that they will remain [b]congruent[/b](the same). Move the vertices to see that they remain congruent. Use a sequence of transformations to show that they are congruent.

What sequence of transformations did you use?

What sequence of transformations could you use to show that △[math]ABC[/math] and △[math]DEF[/math] are congruent? Feel free to check your answer by performing your suggested sequence but it is not required.

Triangle Action

Information: Triangle Action