If the diagnals of a parallelogram are 12 cm arad
16 cm, find the lenghts of each segment of the
diagnals into which they are divided. State the
property of Parlialogram used
Answers
If the diagonals of a parallelogram are equal in length, then is the parallelogram a rectangle?
Answer
10
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8 Answers

Piyush Bansal, Mathematics lover
Answered March 7, 2017
Yes if diagonals of a parallelogram are equal then it is a rectangle.
Let PQRS be a parallelogram. To show that PQRS is a rectangle, we have to prove that one of its interior angles is 90º.
In ΔPQR and ΔSRQ,
PQ = SR (Opposite sides of a parallelogram are equal)
QR = QR (Common)
PR = SQ (Given)
∴ ΔPQR ≅ ΔSRQ (By SSS Congruence rule)
⇒ ∠PQR = ∠SRQ
Since adjacent angles of a parallelogram are supplementary. (Consecutive interior angles)
∠PQR + ∠SRQ= 180º
⇒ ∠PQR + ∠PQR= 180º
⇒ 2∠PQR= 180º
⇒ ∠PQR = 90º
Since PQRS is a parallelogram and one of its interior angles is 90º, PQRS is a rectangle.
please mark me as branilliast
1) Diagonal will divided into 6 cm and 6cm.
2) And the other Diagonal will divided into 8cm nd 8 cm.
Than, by using Pythagoras theorem h^2= b^2+p^2
3)h^2= 6^2+8^2.
h^2= 36cm +64cm
h^2= 100 cm.
h=√100cm
h= 10 cm.