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Question
If in two triangles ABC and PQR, `(AB)/(QR) = (BC)/(PR) = (CA)/(PQ)`, then ΔPQR ∼ ______.
Fill in the Blanks
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Solution
If in two triangles ABC and PQR, `(AB)/(QR) = (BC)/(PR) = (CA)/(PQ)`, then ΔPQR ∼ ΔCAB.
Explanation:
Since `(AB)/(QR) = (BC)/(PR) = (CA)/(PQ)`, the three pairs of corresponding sides are proportional, so by SSS similarity ΔABC ∼ ΔQRP (A↔Q, B↔R, C↔P). Relabeling vertices gives ΔPQR ∼ ΔCAB.
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