Answer to Question #74234 in Geometry for Zoey

Question

https://www.geogebra.org/m/HEvTtDbq

What can you say about the relationship of triangle ABC to triangle DBE? Justify your answer. Will this always be true?

Answer 1

Triangle ABC is similar to triangle DBE: ∆ABC~∆DBE. Due to DE is parallel to AC, angle BDE is equal to angle BAC, and angle BED is equal to angle BCA. Therefore, in conformity with first sign of the similarity of triangles, if two angles of one triangle are equal to two angles of another triangle, they are similar to each other.
∠BDE=∠BAC,∠BED=∠BCA ⇒ ∆ABC~∆DBE.
Answer: triangle ABC is similar to triangle DBE, this will always be true.