Lesson Worksheet: Congruence of Polygons through Transformations Mathematics • 8th Grade
In this worksheet, we will practice identifying congruence of polygons after applying transformations.
Q5:
If triangle is mapped by a rotation about the origin to triangle , would the two triangles be congruent?
- AYes
- BNo
Q7:
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 right and three up
- BA translation two left and three down
- CA translation three right and two down
- DA translation two left and three up
- EA translation two right and three down
Describe the single transformation that would map onto .
- AA translation four right and one down
- BA rotation of counterclockwise about point
- CA translation one right and four down
- DA rotation of clockwise about point
- EA reflection in the line
Hence, are triangles and congruent?
- AYes
- BNo
Q8:
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 up
- Ba translation two right and three up
- Ca translation three right and two up
- Da translation three right and two down
- Ea translation three left and two down
Describe the single transformation that would map onto .
- Aa rotation of counterclockwise about
- Ba translation four right
- Ca rotation of counterclockwise about
- Da rotation of clockwise about
- Ea reflection in the line
Hence, are triangles and congruent?
- ANo
- BYes
Q9:
The figure shows triangles and .
Are the two triangles congruent?
- ANo
- BYes
Justify your answer with one of the following reasons.
- ATriangle can be reflected to obtain triangle and, thus, the triangles are congruent.
- BNo sequence of translations, reflections, or rotations exists that can map triangle onto triangle and, therefore, the two triangles cannot be congruent.
- CTriangle can be rotated to obtain triangle and, thus, the triangles are congruent.
- DWe can apply a two-stage transformation on triangle involving a reflection and then a rotation to obtain triangle and, thus, the triangles are congruent.
Q10:
The figure shows triangles and .
Are the two triangles congruent?
- AYes
- BNo
Justify your answer with one of the following reasons.
- AWe can apply a two-stage transformation on triangle involving a reflection and then a rotation to obtain triangle and, thus, the triangles are congruent.
- BTriangle can be rotated to obtain 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.
Q11:
If triangle is mapped to triangle by a reflection, translation, or rotation, which of the following statements will be true of the two triangles?
- AThey will be similar.
- BThey are the same.
- CThey have exactly one side of the same length.
- DThey will be congruent.
Q12:
Triangle has been reflected in the line to obtain triangle as seen in the given figure.
Are the corresponding angles and sides of the two triangles equal?
- ANo
- BYes
What is the length of ?
What is the length of ?
What is the perimeter of triangle ?
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 rotation about point
- BA counterclockwise rotation about point
- CA clockwise rotation about point
- DA clockwise rotation about point
- EA rotation about point
Describe the single transformation that would map onto .
- AA translation three left and three down
- BA clockwise rotation about point
- CA reflection in the line
- DA counterclockwise rotation about point
- EA clockwise rotation about point
Hence, are triangles and congruent?
- AYes
- BNo
Q14:
The figure shows two triangles and .
Work out the measure of angle .
Work out the measure of angle .
What do you notice about the measures of the angles in both shapes?
- AThe measures of the angles in both triangles depend on their lengths.
- BThe measures of the angles in triangle are half the measures of the angles in triangle .
- CThe measures of the angles in triangle are double the measures of the angles in triangle .
- DThey are equal.
Are the two triangles similar?
- ANo
- BYes
Q15:
The figure shows three triangles: , , and .
Are triangles and similar?
- ANo
- BYes
Justify your answer with one of the following reasons.
- ATriangle can first be translated eight right and two down to and then can be reflected in the line onto ; hence, the triangles are similar.
- BNo sequence of translations, reflections, rotations, or dilations exists that can map triangle onto triangle ; therefore, the two triangles cannot be similar.
Q16:
The figure shows three triangles: , , and .
Are triangles and similar?
- AYes
- BNo
Justify your answer with one of the following reasons.
- ANo sequence of translations, reflections, rotations, or dilations exists that can map triangle onto triangle ; therefore, the two triangles cannot be similar.
- BTriangle can first be translated eight right and two down to and then can be reflected in the line onto ; hence, the triangles are similar.
Q17:
A triangle has vertices at the points , , and . A triangle has vertices at the points , and . By plotting the two triangles and using congruence transformations, decide if the two triangles are congruent.
- AThey are congruent.
- BThey are not congruent.
Q18:
A triangle has vertices at the points , , and . A triangle has vertices at the points , , and . By plotting the two triangles and using congruence transformations, decide if the two triangles are congruent.
- AThey are not congruent.
- BThey are congruent.
Q19:
A triangle has vertices at the points , , and . A triangle has vertices at the points , , and . By plotting the two triangles and using congruence transformations, decide if the two triangles are congruent.
- AThey are congruent.
- BThey are not congruent
Q20:
Triangle has been rotated to obtain triangle as seen in the given figure.
What is the length of ?
What is the length of ?
What type of triangle is ?
- Aequilateral
- Bscalene
- Cisosceles
Q21:
In the given figure, is the image of by reflection in point . Find the length of , rounding your result to the nearest hundredth.
Q22:
Triangle is right-angled at with and . Let be the image of after a translation through 78 cm in the direction of . Let be the image of under a rotation center through angle . Calculate the length to the nearest hundredth.
Q23:
In the given figure, triangle has been reflected to triangle . The perimeter of triangle is 10.5. What is the perimeter of triangle ?
Q24:
Triangle has been rotated about point to obtain triangle as seen in the given figure. Work out the perimeter of triangle .
Q25:
A quadrilateral has been dilated by a scale factor of 2 to . Are and congruent?
- ANo
- BYes