Question

pQRs is a kite in which pQ =PS and QR = SR . SHOW THAT PR is the perpendicular bisector of diagonal Qs.

Answer 1

LET THEM INTERSECT AT POINT O

In triangle PSR and PQR

PS=PQ (GIVEN)
SR=RQ(gIVEN)
PR=RP(COMMON)
SO, THEY ARE CONGRUENT

IN TRIANGLE SPO AND OPQ
SP=PQ(GIVEN)
PO=OP(GIVEN)
ANGLE SPR= ANGLE RPQ(CPCT)
SO, THEY ARE CONGRUENT

HENCE, ANGLE SOP = POQ
ALSO, SOP + POQ=180
SO, THEY ARE 90 DEGREES EACH

AND, SO = OQ (CPCT)

Hence Proved !

Answer 2

in ∆ PSR and ∆ PQR
PS = PQ given
SR = RQ given
PR = PR common
∆ PSR =~ ∆ PQR by SSS
in ∆ SPO and ∆ OPQ
SP = PQ given
PO = PO given
angle SPR = angle RPQ by CPCTC
so, ∆ SOP = ∆ POQ
SOP + POQ = 180°
SOP + 90° = 180°
SOP = 180° - 90°
SOP = 90°
so, they are 90° each
SO = OQ by CPCTC
it's prove...