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°.
संबंधित प्रश्न
The diagonal BD of a parallelogram ABCD bisects angles B and D. Prove that ABCD is a rhombus.
The alongside figure shows a parallelogram ABCD in which AE = EF = FC.
Prove that:
- DE is parallel to FB
- DE = FB
- DEBF is a parallelogram.
In the given figure, ABCD is a parallelogram.
Prove that: AB = 2 BC.
The following figure shows a trapezium ABCD in which AB is parallel to DC and AD = BC. 
Prove that:
(i) ∠DAB = ∠CBA
(ii) ∠ADC = ∠BCD
(iii) AC = BD
(iv) OA = OB and OC = OD.
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
Find the perimeter of the parallelogram PQRS.
In parallelogram ABCD of the accompanying diagram, line DP is drawn bisecting BC at N and meeting AB (extended) at P. From vertex C, line CQ is drawn bisecting side AD at M and meeting AB (extended) at Q. Lines DP and CQ meet at O. Show that the area of triangle QPO is `9/8` of the area of the parallelogram ABCD
Which of the following statement is correct?
In the following figure, ABCD and AEFG are two parallelograms. If ∠C = 55º, determine ∠F.
