Advertisements
Advertisements
प्रश्न
PQRS is a parallelogram. T is the mid-point of PQ and ST bisects ∠PSR.
Prove that: QR = QT
Advertisements
उत्तर
∠PST = ∠TSR ............(i)
∠PTS = ∠TSR ............(ii)(alternate angles ∵ SR || PQ)
From (i) and (ii)
∠PST = ∠PTS
Therefore,
PT = PS
But PT = QT ...(T is midpoint of PQ)
And PS = QR ...(PS and QR are opposite and equal sides of a parallelogram)
Hence,
QT = QR.
APPEARS IN
संबंधित प्रश्न
The diagonal BD of a parallelogram ABCD bisects angles B and D. Prove that ABCD is a rhombus.
Prove that the bisectors of opposite angles of a parallelogram are parallel.
PQRS is a parallelogram. T is the mid-point of PQ and ST bisects ∠PSR.
Prove that: RT bisects angle R
PQRS is a parallelogram. T is the mid-point of PQ and ST bisects ∠PSR.
Prove that: ∠RTS = 90°
ABCD is a parallelogram. The bisector of ∠BAD meets DC at P, and AD is half of AB.
Prove that: ∠APB is a right angle.
In the given figure, MP is the bisector of ∠P and RN is the bisector of ∠R of parallelogram PQRS. Prove that PMRN is a parallelogram.
In the given figure, the perimeter of parallelogram PQRS is 42 cm. Find the lengths of PQ and PS.
Which of the following statement is correct?
In the following figure, ABCD and AEFG are two parallelograms. If ∠C = 55º, determine ∠F.
Construct a parallelogram POUR in which, PO = 5.5 cm, OU = 7.2 cm and ∠O = 70°.
