Question

In the given figure PS is equal to QR and angle SPQ is equal to angle SRQ prove that PR is equal to QR and angle QPR is equal to angle PQS​

Answer 1

Answer:

Step-by-step explanation:

Assumption: Vertices are labeled in order PQRS

with angles SPQ = PQR let these be size C

and sides SP = QR let these be length a

let side PQ be of length b

we generate a symmetric quadrilateral with a line of symmetry through the midpoint of PQ, (which which thus bisects SR)

With S and R effectively fixed in place drawing PR and SQ into your diagram we see two congruent triangles with SAS commonality

in triangle SPQ have side SP and side PQ with included angle SPQ forming the SAS triangle: a-C-b

in triangle PQR have side QR and side PQ with included angle PQR forming the SAS triangle: a-C-b thus congruent. So if angle QPR = A then by congruence PQS also = A

by similar argument SQ = PR = c (continuing the abc ABC side and vertex notation)