Advertisements
Advertisements
प्रश्न
PQRS is a parallelogram. T is the mid-point of PQ and ST bisects ∠PSR.
Prove that: ∠RTS = 90°
Advertisements
उत्तर
∠PST = ∠TSR
∠QRT = ∠TRS
∠QRS + ∠PSR = 180° ...(adjacent angles of || gm are supplementary)
Multiplying by `(1)/(2)`
`(1)/(2)∠"QRS" + (1)/(2)∠"PSR" = (1)/(2) xx x180°`
∠TSR + ∠TRS = 90°
In ΔSTR,
∠TSR + ∠RTS + ∠TRS = 180°
90° + ∠RTS = 180°
∠RTS = 90°.
APPEARS IN
संबंधित प्रश्न
In the given figure, ABCD is a parallelogram.
Prove that: AB = 2 BC.
Points M and N are taken on the diagonal AC of a parallelogram ABCD such that AM = CN. Prove that BMDN is a parallelogram.
PQRS is a parallelogram. T is the mid-point of PQ and ST bisects ∠PSR.
Prove that: QR = QT
PQRS is a parallelogram. T is the mid-point of PQ and ST bisects ∠PSR.
Prove that: RT bisects angle R
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, the perimeter of parallelogram PQRS is 42 cm. Find the lengths of PQ and PS.
Find the perimeter of the parallelogram PQRS.
In the following figure, it is given that BDEF and FDCE are parallelograms. Can you say that BD = CD? Why or why not?
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°.
