# Worksheet: Congruence of Polygons through Transformations

In this worksheet, we will practice identifying congruence of polygons after applying transformations.

**Q1: **

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

Are triangles and similar?

- Ano
- Byes

Are triangles and congruent?

- Ayes
- Bno

**Q3: **

If there exists a combination of rotations, reflections, and translations that would map one shape to another, would the two shapes be congruent?

- Ano
- Byes

**Q5: **

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

- Ayes
- Bno

**Q6: **

A triangle is rotated by about the origin to triangle .

Are triangles and similar?

- Ayes
- Bno

Are triangles and 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