Respuesta :

sqdancefan

Answer:

Only the first pair can be so mapped

Step-by-step explanation:

Reflection across AB and translation will leave the segment corresponding to AB having the same "north-south" (vertical) orientation. The reflection will reverse the clockwise ordering of corresponding vertices.

- selection 2: segment AY is not vertical

- selection 3: the ordering of the vertices is unchanged, not reversed

- selection 4: segment XY is not vertical

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A reflection creates an image that is as far behind from the reflecting line as the preimage is in front of the line

The triangle pair that can be mapped to each other using both translation and reflection across line containing AB is the first triangle pair

Please see the attached diagram

Reason:

First triangle pair;

  • The first figure consists of ΔXYZ and ΔABC that are a reflection of each other across the line AB and a translation

Second triangle pair;

  • The second figure consists of triangle ΔAYC reflected about the line AC Line AC is not parallel to AB, therefore, the ΔAYC cannot be obtained from ΔABC by a reflection across the line AC

Third triangle pair;

  • ΔABC and ΔXYZ have similar orientation, however, triangle ΔABC and ΔXYZ are located on the same side of AB, therefore, a translation only can map triangle ΔABC to ΔXYZ

Fourth triangle pair;

  • Figure four consists of ΔXYZ rotated clockwise and on the same side of line AB as ΔABC, therefore, ΔXYZ cannot be mapped to ΔABC by a reflection and translation

Therefore, the correct option is the first triangle pair figure;

Learn more here:

https://brainly.com/question/10347052

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