Question

P
Ul the theorem.
Theorem : Diagonals of a parallelogram
bisect each other.
Given : OPQRS is a parallelogram
Diagonals PR and QS intersect in point O.
To prove : seg PO = seg RO
R
seg
= seg QO
Proof: In APOS and AROQ
ZOPS = 4 [
side PS = side RO
angles)
side of parallelogram)
ZPSO = 4
angles)
... APSOE AROQ
test)
.: seg PO = seg
.
& seg
seg​

Answer 1

Answer:

PQRS is a parallelogram where PR and QS are diagonals intersect at point O

In △POS and △ROQ

⇒ ∠SPO=∠QRO [ Alternate angles between parallel lines are equal ]

⇒ ∠PSO=∠RQO [ Alternate angles between parallel lines are equal ]

⇒ ∠POS=∠ROQ [ Vertically opposite angles ]

∴ △POS≅△ROQ [ By AAA congruence theorem ]

⇒ segPO≅segRO [ By CPCT ]

⇒ segSO≅segQO [ By CPCT ]