Question

In fig. 5.8 $\square$TAMS is a square, seg AW $\cong$ seg AN then prove that seg SW $\cong$seg SN.

Answer 1

Given: seg AW $\cong$ seg AN
or, AW = AN

Consider $△$ATW and $△$AMN.
$\angle$ATW = $\angle$AMN (90$°$ each)
AW = AN (Given)
AT = AM (All sides of square are equal)

By RHS congruency criteria, $△$ATW $\cong$ $△$AMN
TW = MN (by c.s.c.t.) ...(1)
As, TS= MS (All sides of square are equal) ...(2)
Subtracting eq (1) from eq (2)
TS $-$ TW = MS $-$ MN
WS = NS
or, seg SW $\cong$ seg SN