Question

In the figure given below, $PQR$is an isosceles triangle in which $PQ=PR$, $PQ$and $PR$are produced to $S$and $T$respectively such that $QS=RT$. Show that $RS=QT$

Answer 1

Step-1: Given Information

$PQR$is an isosceles triangle in which $PQ=PR$

also, $QS=RT$

Step-2: Add sides

$PQ$$+QS$and $PR+RT$

$PQ+QS=PS$

$PR+RT=PT$

$\Rightarrow PT=PS$(as $PQ=PR$and $QS=RT$)

Step-3: In $∆PQT$and $∆PRS$

$PQ=PR$(given sides of $∆PQR\hspace{0.17em}$)

$\angle QPT=\angle RPS$(common in both triangles $∆PQT$and $∆PRS$)

$PT=PS$(from Step-2 )

Hence, $∆PQT$$\cong$$∆PRS$ (by $SAS$congruency)

Thus, $RS=QT$(by $CPCT$)