Question

Fill in the Blank.

If in two triangles $PQRandDEF,$ $\mathrm{PR}=\mathrm{EF},\mathrm{QR}=\mathrm{DE},\mathrm{PQ}=\mathrm{FD},$, then $∆\mathrm{PQR}\cong$___.

Answer 1

Proving the congruence of two triangles:

Considering triangles $PQRandDEF,$

$$\begin{gathered} PR=EF \\ QR=DE\left[Given\right] \\ PQ=FD \end{gathered}$$

By Side-Side-Side or SSS congruence property, $∆\mathrm{PQR}\cong ∆FDE$.

Hence, if in two triangles$PQRandDEF$, $\mathrm{PR}=\mathrm{EF},\mathrm{QR}=\mathrm{DE},\mathrm{PQ}=\mathrm{FD},$then $∆\mathrm{PQR}\cong ∆FDE$.