Question

In following pairs of triangles, find the correspondence between the triangles so that they are congruent.

$\text{In}△PQR:PQ=4\text{cm,}QR=5\text{cm,}PR=6\text{cm,}\angle P={60}^{\circ },\angle Q={80}^{\circ },\angle R={40}^{\circ }.$

$\text{In}△XYZ:XY=6\text{cm,}ZY=5\text{cm,}XZ=4\text{cm,}\angle X={60}^{\circ },\angle Y={40}^{\circ },\angle Z={80}^{\circ }$

Answer 1

Let us draw the triangles and write the measures of their corresponding parts along with them.


$\text{From the above figures, we note that}PQ=XZ,QR=YZ,PR=XY\text{and}\angle P=\angle X,\angle Q=\angle Z,\angle R=\angle Y$

$\therefore P\leftrightarrow X,Q\leftrightarrow Z\text{and}R\leftrightarrow Y$

$\text{Hence,}△PQR\cong XZY$