Question

Lennox was curious if triangles \triangle ABE△ABEtriangle, A, B, E and \triangle DCE△DCEtriangle, D, C, E were similar, so she tried to map one figure onto the other using a reflection and a dilation. Lennox concluded: "It's not possible to map \triangle DCE△DCEtriangle, D, C, E onto \triangle ABE△ABEtriangle, A, B, E using a sequence of rigid transformations and dilations, so the triangles are not similar." What error did Lennox make in her conclusion?

Answer 1

Answer:

There is no error. This is a correct conclusion.

Step-by-step explanation:

If a sequence of rigid transformations

(translations, reflections, and rotations) and dilations can map △DCE onto △ABE, then the figures are similar.

Notice that both triangles are right triangles (at vertices B and C), with line AB and DC being the longer legs.

Therefore, if the triangles are similar, we should be able to map each pair of corresponding points onto each other with rigid transformations and dilations:

   D should be mapped onto A.

   C should be mapped onto B.

   E should be mapped onto itself.

Lennox used a reflection across line BE and a dilation about E to get △DCE as close as possible to △ABE. But still, point D did not map onto point A.

So we can conclude that it's not possible to map △DCE onto △ABE using a sequence of rigid transformations and dilations.

Lennox concluded:

"It's not possible to map △DCE onto △ABE using a sequence of rigid transformations and dilations, so the triangles are not similar."

There is no error. This is a correct conclusion.

Answer 2

Answer:

One more transformation – a horizontal stretch – would map ΔDCE onto ΔABE. So the triangles are similar.

Step-by-step explanation:

Rigid transformation involves the applications of some processes and procedures to change the orientation of a given figure. It can either be reflection, translation or rotation. While dilation is the process of resizing a given figure as required.

A horizontal stretching is a transformation that involves changing the position or coordinates of a point along the horizontal axis away from the vertical axis.

Lennox claims he used a sequence of rigid transformations and dilation, but did not perform one more transformation, horizontal stretch, which would make the two triangles to be similar.