Hey 64° angle is bisected buy a really what is the measure of each angle formed

A translation because it can map one angle onto another since dilations preserve angle measures of triangles.

Step-by-step explanation:

In order to prove the two triangles by AA postulate, we must meet the conditions of the AA similarity postulate that says-

"Two triangles that have two congruent angles are similar".

So, we have to prove at least two corresponding angles of the given two triangles congruent.

One triangle is the dilation of the other. When we dilate a figure, the things that change are:

1. Lengths - Dilation changes the lengths of each side of the figure.

2. Size - Dilation changes the size of the figure.

When we dilate a figure, the things that do not change are:

1. Orientation - Dilation preserve orientation

2. Angles - Dilation preserves the interior angles of the figure.

So, the transformation that will preserve both orientation and angles will be used to prove triangles similarity using AA postulate.

Now, the transformations that change orientation are rotation and reflection. So, these transformations can't be used to prove two triangles similar by AA postulate. Thus, options (2) and (4) are eliminated.

The transformations that preserve both angles and orientations are translation and dilation.

Now, option (3) says:"A dilation because it can map one side onto another since dilations preserve side length of triangles."

The above statement is false as dilations don't preserve side lengths.

Now, we are left with option (1).

(1) A translation because it can map one angle onto another since dilations preserve angle measures of triangles.

This is the correct choice.

A translation only moves the entire figure and thus we can overlap the vertices of the triangle and find whether the angles are congruent or not.

With the translation we will prove that other pair of angles of the triangles are congruent and thus the two triangles can be proved similar using the AA similarity postulate.