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Worksheet: Congruence of Triangles Through Rigid Transformations

Q1:

If triangle is mapped by a reflection in the line to triangle , would the two triangles be congruent?

  • A yes
  • B no

Q2:

If triangle is mapped by a rotation about the origin to triangle , would the two triangles be congruent?

  • A yes
  • B no

Q3:

Determine, by applying transformations, whether the two triangles seen in the given figure are congruent.

  • A They are congruent.
  • B They are not congruent.

Q4:

Determine, by applying transformations, whether the two triangles seen in the given figure are congruent.

  • A They are not congruent.
  • B They are congruent.

Q5:

Determine, by applying transformations, whether the two triangles seen in the given figure are congruent.

  • A They are congruent.
  • B They are not congruent.

Q6:

Determine, by applying transformations, whether the two triangles seen in the given figure are congruent.

  • A They are congruent.
  • B They are not congruent.

Q7:

In the given figure, a reflection in the line would map triangle to triangle . Does it follow that the two triangles congruent?

  • A yes
  • B no

Q8:

A triangle has been dilated from a center by a scale factor of 3 to triangle .

Are triangles and similar?

  • Ayes
  • Bno

Are triangles and congruent?

  • Ano
  • Byes

Q9:

A triangle is rotated by about the origin to triangle .

Are triangles and similar?

  • Ayes
  • Bno

Are triangles and congruent?

  • Ayes
  • Bno

Q10:

The figure shows triangles and .

Are the two triangles congruent?

  • Ayes
  • Bno

Justify your answer with one of the following reasons.

  • ATriangle can be reflected onto triangle and, thus, the triangles are congruent.
  • BTriangle can be translated onto triangle and, thus, the triangles are congruent.
  • CNo sequence of translations, reflections, or rotations exists that can map triangle onto triangle and, therefore, the two triangles cannot be congruent.
  • DTriangle can be rotated onto triangle and, thus, the triangles are congruent.

Q11:

The figure shows triangles and .

Are the two triangles congruent?

  • Ayes
  • Bno

Justify your answer with one of the following reasons.

  • ATriangle can be rotated onto triangle and, thus, the triangles are congruent.
  • BTriangle can be translated onto triangle and, thus, the triangles are congruent.
  • CNo sequence of translations, reflections, or rotations exists that can map triangle onto triangle and, therefore, the two triangles cannot be congruent.
  • DTriangle can be reflected onto triangle and, thus, the triangles are congruent.

Q12:

The two triangles in the given figure share the measures of two angles and the length of one side. Does a rigid transformation exist that would map triangle to triangle , and, hence, are the two triangles congruent?

  • A yes
  • B no

Q13:

The triangle has been transformed onto triangle which has then been transformed onto triangle as seen in the figure.

Describe the single transformation that would map onto .

  • Aa translation two left and three up
  • Ba translation three right and two down
  • Ca translation two right and three up
  • Da translation two right and three down
  • Ea translation two left and three down

Describe the single transformation that would map onto .

  • Aa reflection in the line
  • Ba rotation of clockwise about point
  • Ca translation one right and four down
  • Da translation four right and one down
  • Ea rotation of counterclockwise about point

Hence, are triangles and congruent?

  • Ano
  • Byes

Q14:

The triangle has been transformed onto triangle which has then been transformed onto triangle as seen in the figure.

Describe the single transformation that would map onto .

  • Aa translation three left and two down
  • Ba translation two right and three up
  • Ca translation three left and two up
  • Da translation three right and two up
  • Ea translation three right and two down

Describe the single transformation that would map onto .

  • Aa reflection in the line
  • Ba translation four right
  • Ca rotation of clockwise about
  • Da rotation of counterclockwise about
  • Ea rotation of counterclockwise about

Hence, are triangles and congruent?

  • Ano
  • Byes

Q15:

The triangle has been transformed onto triangle which has then been transformed onto triangle as seen in the figure.

Describe the single transformation that would map to .

  • Aa rotation of about
  • Ba rotation of about
  • Ca rotation of clockwise about point
  • Da reflection in the line
  • Ea rotation of clockwise about point

Describe the single transformation that would map to .

  • Aa rotation of clockwise about point
  • Ba rotation of clockwise about point
  • Ca translation two right
  • Da rotation of counterclockwise about point
  • Ea rotation of counterclockwise about point

Hence, are triangles and congruent?

  • Ano
  • Byes

Q16:

The triangle has been transformed onto triangle which has then been transformed onto triangle then transformed onto as seen in the figure.

Describe the single transformation that would map onto .

  • Aa counterclockwise rotation about
  • Ba clockwise rotation about
  • Ca clockwise rotation about
  • Da counterclockwise rotation about
  • Ea translation one left and three up

Describe the single transformation that would map onto .

  • Aa reflection in the line
  • Ba translation two up
  • Ca clockwise rotation about
  • Da clockwise rotation about
  • Ea rotation about

Describe the single transformation that would map onto .

  • Aa translation three left and two down
  • Ba translation two left and three up
  • Ca translation three left and two up
  • Da translation three right and two down
  • Ea translation two right and three down

Hence, are triangles and congruent?

  • Ano
  • Byes