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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?
- Ayes
- Bno
Q2:
If triangle is mapped by a rotation about the origin to triangle , would the two triangles be congruent?
- Ayes
- Bno
Q3:
Determine, by applying transformations, whether the two triangles seen in the given figure are congruent.
- AThey are congruent.
- BThey are not congruent.
Q4:
Determine, by applying transformations, whether the two triangles seen in the given figure are congruent.
- AThey are not congruent.
- BThey are congruent.
Q5:
Determine, by applying transformations, whether the two triangles seen in the given figure are congruent.
- AThey are congruent.
- BThey are not congruent.
Q6:
Determine, by applying transformations, whether the two triangles seen in the given figure are congruent.
- AThey are congruent.
- BThey 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?
- Ayes
- Bno
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 rotated onto triangle and, thus, the triangles are congruent.
- CTriangle can be translated onto triangle and, thus, the triangles are congruent.
- DNo sequence of translations, reflections, or rotations exists that can map triangle onto triangle and, therefore, the two triangles cannot be 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 reflected onto triangle and, thus, the triangles are congruent.
- CTriangle can be translated onto triangle and, thus, the triangles are congruent.
- DNo sequence of translations, reflections, or rotations exists that can map triangle onto triangle and, therefore, the two triangles cannot be 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?
- Ayes
- Bno
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 down
- Ba translation two right and three up
- Ca translation two right and three down
- Da translation two left and three up
- Ea translation three right and two down
Describe the single transformation that would map onto .
- Aa rotation of counterclockwise about point
- Ba rotation of clockwise about point
- Ca reflection in the line
- Da translation one right and four down
- Ea translation four right and one down
Hence, are triangles and congruent?
- Ayes
- Bno
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 right and two down
- Ba translation three left and two up
- Ca translation three right and two up
- Da translation three left and two down
- Ea translation two right and three up
Describe the single transformation that would map onto .
- Aa rotation of counterclockwise about
- Ba translation four right
- Ca reflection in the line
- Da rotation of clockwise about
- Ea rotation of counterclockwise about
Hence, are triangles and congruent?
- Ayes
- Bno
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 clockwise about point
- Ba rotation of clockwise about point
- Ca reflection in the line
- Da rotation of about
- Ea rotation of about
Describe the single transformation that would map to .
- Aa rotation of counterclockwise about point
- Ba rotation of clockwise about point
- Ca rotation of clockwise about point
- Da translation two right
- Ea rotation of counterclockwise about point
Hence, are triangles and congruent?
- Ayes
- Bno
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 translation one left and three up
- Ba clockwise rotation about
- Ca counterclockwise rotation about
- Da counterclockwise rotation about
- Ea clockwise rotation about
Describe the single transformation that would map onto .
- Aa rotation about
- Ba translation two up
- Ca reflection in the line
- Da clockwise rotation about
- Ea clockwise rotation about
Describe the single transformation that would map onto .
- Aa translation three left and two down
- Ba translation two right and three down
- Ca translation three left and two up
- Da translation three right and two down
- Ea translation two left and three up
Hence, are triangles and congruent?
- Ayes
- Bno
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