Question

If in two triangles DEF and PQR, ∠D = ∠Q and ∠R = ∠E, then `(DE)/(QR) = (DF)/(PQ)` = ______.

Answer 1

If in two triangles DEF and PQR, ∠D = ∠Q and ∠R = ∠E, then `(DE)/(QR) = (DF)/(PQ)` = `underlinebb((EF)/(PR))`.

Explanation:

∠D = ∠Q and ∠R = ∠E ⇒ two angles of one triangle equal two angles of the other, so the triangles are similar by AA. Similar triangles have their corresponding sides in proportion; here D↔Q, E↔R, F↔P, so `(DE)/(QR) = (DF)/(PQ) = (EF)/(PR)`.