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Constructions & proofs

Proofs with similar triangles

1 / 5Standard

In △ABC, point D is on side AB and point E is on side AC such that DE // BC. The proof that △ADE ∽ △ABC is written as follows:

[Proof]

In △ADE and △ABC,

Since DE // BC, corresponding angles of parallel lines are equal, so

∠ADE = ∠ABC ... (1)

∠AED = ∠ACB ... (2)

From (1) and (2), since ( ),

△ADE ∽ △ABC.

Which of the following is the most appropriate similarity condition to fill in the blank?