Is there a method that could prove that these two triangles are similar?

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a
yes, a sequence of dilations and rigid motions carries one triangle onto the other.

b
yes, showing that all pairs of corresponding sides are congruent.

c
no, the triangles are not similar because we do not know the measurement of third angle.

d
no, the triangles are not similar due to differences in size and side lengths.

  A  Yes, a sequence of dilations and rigid motions carries one triangle onto the other

Step-by-step explanation:

Since two angles are marked with the same measures in each triangle, the triangles are similar by the AA postulate with no further action.

By some accounts it seems to be necessary to lay one figure on top of the other to demonstrate similarity. In order to do that, the smaller triangle would need to be dilated and translated (a rigid motion) to make it occupy the same space as the larger triangle.

step-by-step explanation: