Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
∠DAP =∠PAB
∠CBP = ∠PBA
∠DAB + ∠CBA = 180° ...(adjacent angles of || gm are supplementary)
Multipying by `(1)/(2)`
`(1)/(2)∠"DAB" + (1)/(1)∠"CBA" = (1)/(2) xx 180°`
∠PAB + ∠PBA = 90°
In ΔAPB,
∠PAB + ∠PBA + ∠APB = 180°
90° + ∠APB = 180°
∠APB = 90°
Therefore, ∠APB is a right angle.
संबंधित प्रश्न
In the alongside diagram, ABCD is a parallelogram in which AP bisects angle A and BQ bisects angle B.
Prove that:
- AQ = BP
- PQ = CD
- ABPQ is a parallelogram.
Prove that the bisectors of opposite angles of a parallelogram are parallel.
In parallelogram ABCD, the bisector of angle A meets DC at P and AB = 2 AD.
Prove that:
(i) BP bisects angle B.
(ii) Angle APB = 90o.
PQRS is a parallelogram. T is the mid-point of PQ and ST bisects ∠PSR.
Prove that: QR = QT
ABCD is a parallelogram. The bisector of ∠BAD meets DC at P, and AD is half of AB.
Prove that: BP bisects ∠ABC.
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 a parallelogram ABCD, E is the midpoint of AB and DE bisects angle D. Prove that: BC = BE.
Find the perimeter of the parallelogram PQRS.
In the Figure, ABCD is a rectangle and EFGH is a parallelogram. Using the measurements given in the figure, what is the length d of the segment that is perpendicular to `bar("HE")` and `bar("FG")`?
Which of the following statement is correct?
