Question

question 2 (multiple choice worth 2 points) (03.09r mc) use △abc below to answer the question that follows: image of triangle abc with points d on ab and e on bc, and segment de which fact is not used to prove that abc is similar to dbe? the sum of angles a and b are supplementary to angle c. segments ac and de are parallel. ab is a transversal line passing ac and de. angle b is congruent to itself due to the reflexive property.

Explanation:

To prove \(\triangle ABC \sim \triangle DBE\), we use:

• \(AC \parallel DE\) (gives corresponding angles congruent, e.g., \(\angle C \cong \angle DEB\), \(\angle A \cong \angle EDB\)) via the Basic Proportionality Theorem or AA similarity.
• \(AB\) as a transversal (creates equal corresponding angles or alternate interior angles).
• Reflexive property (\(\angle B \cong \angle B\)).

The fact that \(\angle A + \angle B\) is supplementary to \(\angle C\) is a triangle angle - sum property (\(\angle A+\angle B+\angle C = 180^{\circ}\), so \(\angle A+\angle B=180^{\circ}-\angle C\)) but is not needed to establish similarity (which relies on angle - angle correspondence, not the angle - sum relation for \(\triangle ABC\) alone).

Answer:

A. The sum of angles A and B are supplementary to angle C.