Question

In ΔABC and ΔPQR, in a one to one correspondence of vertices, `(AB)/(QR) = (BC)/(PR) = (CA)/(PQ)`, then ______ statement is true.

Options

• ΔPQR ~ ΔABC

• ΔPQR ~ ΔCAB

• ΔCBA ~ ΔPQR

• ΔBCA ~ ΔPQR

Answer 1

In ΔABC and ΔPQR, in a one to one correspondence of vertices, `(AB)/(QR) = (BC)/(PR) = (CA)/(PQ)`, then ΔPQR ~ ΔCAB statement is true.

Explanation:

`(AB)/(QR) = (BC)/(PR) = (CA)/(PQ)`

This means the corresponding sides are proportional, so by the SSS similarity criterion, the triangles are similar. 

• AB corresponds to QR
• BC corresponds to RP (or PR)
• CA corresponds to PQ

So the correct correspondence of vertices is: ΔPQR ~ ΔCAB