Question

Use Δabc below to answer the question that follows: triangle abc with sides ba and bc intersected by line de. Which fact is not used to prove that abc is similar to dbe?

1) The sum of angles a and b are supplementary to angle c.
2) Segments ac and de are parallel.
3) Ab is a transversal line passing ac and de.
4) Angle b is congruent to itself due to the reflexive property.

Answer 1

The fact that the sum of angles A and B are supplementary to angle C is not used to prove that triangles ABC and DBE are similar because it doesn't address the relationship between the two triangles.

Step-by-step explanation:

To determine which fact is not used to prove that triangles ABC and DBE are similar, let's consider each statement:

1. The sum of angles A and B are supplementary to angle C. This is true for any triangle, as the sum of the angles in a triangle is 180 degrees, but it doesn't prove similarity.
2. Segments AC and DE are parallel. If these segments are parallel, then corresponding angles created by a transversal line are congruent, which is a key fact in proving similarity.
3. AB is a transversal line passing AC and DE. This statement supports the idea that parallel lines are cut by a transversal, which creates corresponding angles that are congruent, aiding the proof of similarity.
4. Angle B is congruent to itself due to the reflexive property. This is true and is often used in geometric proofs, including those for similarity.

Based on the above analysis, the fact that is not used to prove that triangles ABC and DBE are similar is statement 1. This statement simply describes the relationship of angles within a single triangle and doesn't address the relationship between the two triangles in question.