The correct choice is the diagram where △ABC and △DEC are drawn so that two pairs of corresponding angles are clearly marked congruent, with both triangles sharing angle C (or another common vertex), allowing you to use the AA similarity criterion.

Key idea: AA similarity

To prove △ABC ∼ △DEC using similarity transformations, you want a diagram that makes Angle-Angle (AA) similarity obvious. That means:

  • One angle in △ABC is marked congruent to one angle in △DEC (for example, ∠A ≅ ∠D).
  • A second angle in △ABC is marked congruent to a second angle in △DEC (often they share ∠C, so ∠ACB and ∠DCE are the same angle or both marked congruent).
  • Once two pairs of corresponding angles are congruent, the triangles are similar by AA, and a similarity transformation (rotation, reflection, translation, dilation) can map △ABC onto △DEC.

In many multiple‑choice versions of this problem, that ends up being “the first diagram,” i.e., the one with clearly marked matching angles in both triangles, not the one focusing only on sides or just one right angle.

What that diagram usually looks like

You can picture the “right” diagram like this:

  • △ABC and △DEC either share vertex C or are drawn so that angle at C in both triangles is indicated as equal.
  • Another pair of angles is marked equal, such as ∠A in △ABC and ∠D in △DEC.
  • The orientation might be different (one triangle rotated or flipped), but angle markings line up the correspondence: A ↔ D, B ↔ E, C ↔ C.

This makes it natural to justify that a rotation/reflection plus dilation carries one triangle to the other, confirming similarity.

Why other diagrams are usually wrong

In the versions discussed in online help and prep sites, the incorrect diagrams typically:

  • Show only one pair of equal angles (not enough for AA).
  • Emphasize side lengths without actual proportionality indicated.
  • Make the triangles share a right angle but fail to mark any second angle correspondence.

Those do not give you enough information to claim a similarity transformation exists.

Mini example story

Imagine a coordinate grid where △ABC is a small triangle near the origin and △DEC is a larger triangle above it.

If both triangles have ∠C as the same physical angle, and ∠A is marked equal to ∠D, then you could:

  1. Rotate △ABC so that its sides line up with those of △DEC.
  2. Dilate it from point C until its sides match the length ratios of △DEC.

That sequence of similarity transformations shows △ABC ∼ △DEC, and it’s exactly what the “right” diagram is hinting at.

HTML table: what to look for in the diagram

html

<table>
  <tr>
    <th>Feature in diagram</th>
    <th>Why it matters for △ABC ∼ △DEC</th>
  </tr>
  <tr>
    <td>Two pairs of corresponding angles marked congruent</td>
    <td>Gives AA similarity, enough to prove the triangles are similar via transformations.[web:3][web:5][web:6]</td>
  </tr>
  <tr>
    <td>Shared angle at C (both triangles meet at C)</td>
    <td>Automatically provides one common angle; only one more pair is needed for AA.[web:3][web:6][web:9]</td>
  </tr>
  <tr>
    <td>Triangles may be rotated/reflected</td>
    <td>Allows a rotation or reflection as part of the similarity transformation while preserving corresponding angles.[web:1][web:8][web:9]</td>
  </tr>
  <tr>
    <td>Optional proportional side indication</td>
    <td>Supports SSS or SAS similarity, but AA from the angle markings is usually the intended path.[web:1][web:4][web:8]</td>
  </tr>
</table>

TL;DR: Choose the diagram where △ABC and △DEC have two pairs of matching angle markings (often sharing angle C); that’s the one you can use to prove △ABC ∼ △DEC by similarity transformations using AA.📐

Information gathered from public forums or data available on the internet and portrayed here.