Q. PQRS is a rectangle in which diagonal PR bisect P and Q. Show that
PQRS is a square
Diagonal QR bisect Q and S
Answers
To find ∠PQO and ∠PSQ.
PQRS is a rectangle, and O is the intersection point of diagonals PR and SQ.
PR=SQ [Diagonals of rectangle are equal]
PO=Qo [Diagonals of rectangle bisect each other]
∴∠PQO=∠OPQ→(1) [Angles opposite to equal sides]
In △POQ ,
∠PQO+∠POQ+∠OPQ=180
∘
2∠PQO+110
∘
=180
∘
[From (1)]
∠PQO=
2
180
∘
−110
∘
=35
∘
Now, in △PQS
∠PQS+∠QPS+∠PSQ=180
∘
35
∘
+90
∘
+∠PSQ=180
∘
∠PSQ=180
∘
−125
∘
=55
∘
Please mark me as brainliest
Step-by-step explanation:
To find ∠PQO and ∠PSQ.
PQRS is a rectangle, and O is the intersection point of diagonals PR and SQ.
PR=SQ [Diagonals of rectangle are equal]
PO=Qo [Diagonals of rectangle bisect each other]
∴∠PQO=∠OPQ→(1) [Angles opposite to equal sides]
In △POQ ,
∠PQO+∠POQ+∠OPQ=180
∘
2∠PQO+110
∘
=180
∘
[From (1)]
∠PQO=
2
180
∘
−110
∘
=35
∘
Now, in △PQS
∠PQS+∠QPS+∠PSQ=180
∘
35
∘
+90
∘
+∠PSQ=180
∘
∠PSQ=180
∘
−125
∘
=55
∘
