What additional information could be used to prove that △abc ~ △nml? check all that apply. a) ∠b ≅ ∠mb) △abc is a right triangle. c) △abc was rotated and dilated by a scale factor between 0 and 1.d) △abc was translated right and down. e) ∠c ≅ ∠l

Answers are A, C and E

Step-by-step explanation:

For two triangles to be similar, we must have corresponding angles equal.

Or the sides corresponding are proportional.

So when Triangle ABC is similar to triangle NML, we have corresponding angles as (A,N) (B,M) and (C,L).  Of these it is sufficient to have any two equal, since third will automatically be equal.

So Option A angle B and M equal is necessary.

Also option E, angle C = angle L is necessary

Corresponding sides are (AB, NM) (BC, ML) and (AC,NL).

When a triangle is rotated and dilated by a scale factor we will get corresponding sides proportional and the constant of proportion would be scale factor.

So we have option C is also right.

A,C and E are right.

We know that two figures are congruent if the figures have the same shape but different sizes.

The correct options are A, C, and E.

Particularly for triangles, two triangles are congruent if the measures of the interior angles are equal.

Here we can see that we have two right triangles, and we want to see what extra information would imply that the triangles are congruent.

A) ∠B ≅ ∠M

If two angles (not the 90° ones) are equal, we also know that both triangles have the 90° angles equal, then the third pair of angles must also be equal, meaning that the triangles are congruent.

C) △ABC was rotated and dilated by a scale factor between 0 and 1.

This would imply that triangle ABC was only translated an reduced in size to generate NML, then the shape is non-changed, this would imply that the figures are congruent.

E) ∠C ≅ ∠L

Exact same reasoning as in A.

Option B is trivial, so it does not add any useful information, option D is false, as we can see the orientations are different.

Then the correct options are:

A, C, and E.

If you want to learn more, you can read:

link

step-by-stp

the correct answer is the section c