Question

If in two triangles DEF and PQR, ∠D = ∠Q and ∠R = ∠E, then $\frac{DE}{QR}=\frac{DF}{PQ}$ = _________.

Answer 1

In ∆DEF and ∆PQR,

∠D = ∠Q (Given)

∠E = ∠R (Given)

∴ ∆DEF $~$ ∆QRP (AA Similarity criterion)

$\Rightarrow \frac{\mathrm{DE}}{\mathrm{QR}}=\frac{\mathrm{DF}}{\mathrm{QP}}=\frac{\mathrm{EF}}{\mathrm{RP}}$ (If two triangles are similar, then their corresponding sides are proportional)

If in two triangles DEF and PQR, ∠D = ∠Q and ∠R = ∠E, then $\frac{\mathrm{DE}}{\mathrm{QR}}=\frac{\mathrm{DF}}{\mathrm{PQ}}=\underline{\frac{\mathrm{EF}}{\mathrm{RP}}}$.