Question

complete each statement to show why △dea ~ △cba. step 1: ∠dea is congruent to ∠cba because they are both right angles. step 2: ∠ead is congruent to ∠bac because they are vertical angles. now, how do you know that △dea ~ △cba? triangles that have two pairs of congruent angles are always similar. two right triangles are always similar. triangles formed by intersecting lines are always similar.

Explanation:

To determine why \(\triangle DEA \sim \triangle CBA\), we analyze the angles:

• Step 1 shows \(\angle DEA \cong \angle CBA\) (both right angles).
• Step 2 shows \(\angle EAD \cong \angle BAC\) (vertical angles).

By the AA (Angle - Angle) Similarity Criterion, if two triangles have two pairs of congruent angles, they are similar. The other options are incorrect: two right triangles are not always similar (they need proportional sides or another congruent angle), and triangles formed by intersecting lines are not always similar (this is not a valid similarity rule). Thus, the correct reason is that triangles with two pairs of congruent angles are always similar.

Answer:

Triangles that have two pairs of congruent angles are always similar.