Question

7.
PQR and SQR are isosceles triangles on the same base QR (Fig. 11.37). Prove
that ZPQS = ZPRS.
P
R.
S​

Answer 1

$\fbox\orange{A}\fbox\pink{N}\fbox\blue{S}\fbox\red{W}\fbox\purple{E}\fbox\red{R}$

given: PQR and SQR are isos. triangles

to prove: angle PQS = angle PRS

proof:

since

SQ =SR therefore

angle RQS= angle QRS....(angle opposite to equal sides are equal) (1)

similarly

angle PQR= angle PRQ....(above reason)

(2)

adding (1) and (2)

angle RQS + angle PQR = angle QRS + angle PRQ

gives:

angle PQS= angle PRS

Hence Prooved.