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Question
If in two triangles ABC and PQR, `(AB)/(QR) = (BC)/(PR) = (CA)/(PQ)`, then ______.
Options
ΔPQR ~ ΔCAB
ΔPQR ~ ΔABC
ΔCBA ~ ΔPQR
ΔBCA ~ ΔPQR
Solution
If in two triangles ABC and PQR, `(AB)/(QR) = (BC)/(PR) = (CA)/(PQ)`, then ΔPQR ~ ΔCAB.
Explanation:
Given, in two ΔABC and ΔPQR,
`("AB")/("QR") = ("BC")/("PR") = ("CA")/("PQ")`
Which shows that sides of one triangle are proportional to the side of the other triangle, then their corresponding angles are also equal, so by SSS similarity, triangles are similar.
i.e., ΔCAB ∼ ΔPQR
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