# 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

• 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

• 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 .

• 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 .

• Ea translation one left and three up

Describe the single transformation that would map onto .

• Aa reflection in the line
• Ba translation two up