Worksheet: Congruence of Triangles Through Rigid Transformations

Practice identifying congruent triangles using transformations. This worksheet reinforces that reflections, rotations, and translations produce an image that is congruent to the object, and dilations produce an image that is similar to the object.

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